OPINION

Defendants Corinthian Colleges, Inc., and related entities appeal the district court’s partial denial of their motion to compel arbitration. Plaintiffs, former students at for-profit schools owned by Corinthian, brought this putative class action on behalf of current and former students, alleging that Corinthian engaged in a deceptive scheme to entice the enrollment of prospective students in violation of California law. Pursuant to arbitration clauses in Plaintiffs’ enrollment agreements, Corinthian moved to compel arbitration. The district court granted the motion in part but denied the motion regarding Plaintiffs’ claims for injunctive relief under California’s unfair competition law, false advertising law, and Consumer Legal Remedies Act. In doing so, the district court relied on decisions by the California Supreme Court establishing the so-called Broughtour-Cruz rule, which exempts claims for “public injunctive relief’ from arbitration.

Based on decisions of the United States Supreme Court, including some rendered after the district court entered its order in this case and after the California Supreme Court decisions establishing the Broughton-Cruz rule, we conclude that the Broughtorir-Cruz rule is preempted by the Federal Arbitration Act. We reverse that portion of the district court’s ruling. The district court is instructed to direct all of Plaintiffs’ claims to arbitration and to stay the action pending arbitration.

I. Background

Kevin Ferguson is a graduate of Everest Institute of Miami’s Medical Assistant Program. He enrolled in the program in June 2009 and attended Everest for approximately one year. He allegedly financed his education through federal student loans and, despite graduating with a strong academic record, was unable to find employment in the medical assistant field.

Sandra Muniz attended Heald College in California in 2007, 2008 and 2009. After completing a business skills certificate, she enrolled in a paralegal program that she did not complete. She later enrolled in a criminal justice program. Like Ferguson, Muniz alleged that she financed her education through student loans and was unable to find meaningful employment.

Ferguson and Muniz brought two separate putative class actions against Corinthian, the .parent company of the schools they attended. Corinthian also owns and operates a number of other for-profit academic institutions nationwide, many operating under the names “Everest” and “Heald.” Plaintiffs’ proposed class included all students in the United States and Canada who enrolled in an Everest school after approximately January 24, 2005, or a Heald school after approximately January 24, 2009. The district court.consolidated Ferguson’s and Muniz’s cases into the present action.

The thrust of Plaintiffs’ complaints was that Corinthian systematically misled prospective students in order to entice enrollment. Corinthian allegedly misrepresented the quality of its education, its accreditation, the career prospects for its graduates, and the actual cost of education at one of its schools. Students were also allegedly misinformed about financial aid, which resulted in student loans that many could not repay. Corinthian also allegedly targeted veterans and military personnel specifically, so that it could receive funding through federal financial aid programs available to those people.

Plaintiffs asserted seven claims under California law. At issue in this appeal are Plaintiffs’ claims under California’s unfair competition law (“UCL”), California Business and Professions Code § 17200 et seq.; false advertising law (“FAL”), California Business and Professions Code § 17500 et seq.; and Consumer Legal Remedies Act (“CLRA”), California Civil Code § 1750 et seq. Plaintiffs sought both money damages and injunctive relief under those statutes.

Plaintiffs’ enrollment agreements each contained an arbitration clause. Additionally, Ferguson signed an “Enrollment Agreement Addendum” containing an arbitration clause, and Muniz signed an “Agreement to Binding Arbitration and Waiver of Jury Trial.” Based on those agreements, Corinthian moved to compel arbitration of the entire action.

The district court granted the motion with respect to most of Plaintiffs’ claims and stayed those claims pending arbitration. Applying California’s BroughtonCruz rule, the court declined to compel arbitration of Plaintiffs’ requests for injunctive relief under the UCL, FAL, and CLRA, though it sent Plaintiffs’ requests for damages under those statutes to arbitration. Corinthian appealed that ruling.

II. Discussion

We review de novo a district court’s denial of a motion to compel arbitration. Kilgore v. KeyBank, Nat’l Ass’n, 718 F.3d 1052, 1057 (9th Cir.2013) (en banc).

A. The Federal Arbitration Act

The Federal Arbitration Act (“FAA”) provides that agreements to arbitrate are “valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract.” 9 U.S.C. § 2 . That statute reflects an “emphatic federal policy” in favor of arbitration. Marmet Health Care Ctr., Inc. v. Brown, — U.S. -, 132 S.Ct. 1201, 1203 , 182 L.Ed.2d 42 (2012) (per curiam) (citation omitted). Its purpose is to “ensur[e] that private arbitration agreements are enforced.” Mortensen v. Bresnan Commc’ns, LLC, 722 F.3d 1151, 1159 (9th Cir.2013) (quoting AT&T Mobility LLC v. Concepcion, — U.S. -, 131 S.Ct. 1740 , 1748, 179 L.Ed.2d 742 (2011)).

Pursuant to the Supremacy Clause of the United States Constitution, “the FAA preempts contrary state law.” Id. at 1158. In enacting the FAA, Congress “withdrew the power of the states to require a judicial forum for the resolution of claims which the contracting parties agreed to resolve by arbitration.” Southland Corp. v. Keating, 465 U.S. 1, 10 , 104 S.Ct. 852 , 79 L.Ed.2d 1 (1984). We are thus prohibited from applying any state statute that invalidates an arbitration agreement. Allied-Bruce Terminix Cos., Inc. v. Dobson, 513 U.S. 265, 272 , 115 S.Ct. 834 , 130 L.Ed.2d 753 (1995). Nor may we apply any other state law that “prohibits outright the arbitration of a particular type of claim.” Concepcion, 131 S.Ct. at 1747.

Corinthian argues that the FAA preempts California’s Broughton-Cruz rule. We agree.

B. The Broughton-Cruz Rule

The Broughton-Cruz rule began with the California Supreme Court’s decision in Broughton v. Cigna Healthplans of California, 21 Cal.4th 1066 , 90 Cal.Rptr.2d 334 , 988 P.2d 67 (1999). Broughton involved claims by a minor and his mother against a health care company, Cigna Healthplans of California. Id., 90 Cal.Rptr.2d 334 , 988 P.2d at 71 . The minor plaintiff suffered severe injuries at birth, which the plaintiffs alleged were caused by substandard prenatal medical care and the denial of a medically necessary cesarean delivery. Id. In addition to asserting a medical malpractice claim, the plaintiffs alleged that Cigna had violated the CLRA by deceptively and misleadingly advertising the quality of its medical services. Id. They sought damages and an order enjoining Cigna’s deceptive practices. Id.; see also Kilgore, 718 F.3d at 1059-60 (summarizing Broughton).

The CLRA, which is intended to “protect consumers against unfair and deceptive business practices and to provide efficient and economical procedures to secure such protection,” gives private parties the right to seek an order enjoining practices that violate it. Broughton, 90 Cal.Rptr.2d 334 , 988 P.2d at 74 (citations omitted); see also Cal. Civil Code §§ 1760 , 1780. When a plaintiff exercises that right, it functions as a “private attorney general, enjoining future deceptive practices on behalf of the general public.” Broughton, 90 Cal.Rptr.2d 334 , 988 P.2d at 76 .

Because of an “inherent conflict” between arbitration and the purposes of the CLRA, the California Supreme Court held that arbitration could not be compelled for such claims for a “public injunction.” Id., 90 Cal.Rptr.2d 334 , 988 P.2d at 77, 78 . The California court identified two factors that create the- conflict. First, public injunctions under the CLRA are “for the benefit of the general public rather than the party bringing the action,” and, second, the “judicial forum has significant institutional advantages over arbitration in administering a public injunctive remedy, which as a consequence will likely lead to the diminution or frustration of the public benefit if the remedy is entrusted to arbitrators.” Id.

The California Supreme Court adopted the “inherent conflict” analysis from the United States Supreme Court. Id., 90 Cal. Rptr.2d 334 , 988 P.2d at 73-74 . The United States Supreme Court had earlier explained that some statutory claims are not “suitable” for arbitration, and that suitability depends on congressional intent. Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 627-28 , 105 S.Ct. 3346 , 87 L.Ed.2d 444 (1985). Identifying an “ ‘inherent conflict’ between arbitration and the [statute’s] underlying purposes” is one way of demonstrating that Congress did not intend for claims brought under that statute to be arbitrated. Gilmer v. Interstate/Johnson Lane Corp., 500 U.S. 20, 26 , 111 S.Ct. 1647 , 114 L.Ed.2d 26 (1991) (quoting Shearson/Am. Express Inc. v. McMahon, 482 U.S. 220, 227 , 107 S.Ct. 2332 , 96 L.Ed.2d 185 (1987)).

In Cruz v. PacifiCare Health Systems, Inc., 30 Cal.4th 303 , 133 Cal.Rptr.2d 58 , 66 P.3d 1157, 1164-65 (2003), the California Supreme Court extended its holding in Broughton to requests for public injunctive relief under the UCL and FAL. Under the UCL, “any person engaged in unfair competition may be enjoined,” and an action to enforce that statute may be “brought by a public prosecutor or by any person acting for the interests of itself, its members or the general public.” Id., 133 Cal.Rptr.2d 58 , 66 P.3d at 1164 (internal quotation marks and citations omitted); see also Cal. Bus. & Prof.Code §§ 17203, 17204. The FAL, which makes unlawful “untrue or misleading statements” designed to induce the purchase of goods and services, similarly authorizes the enjoining of such statements by members of the public. Cruz, 133 Cal.Rptr.2d 58 , 66 P.3d at 1164 (citations omitted); see also Cal. Bus. & Prof.Code §§ 17500, 17535.

This court applied the Broughton-Cruz rule in Davis v. O’Melveny & Myers, 485 F.3d 1066 (9th Cir.2007). Davis involved an employee’s claims against her employer under various federal and California statutes, including the UCL. Id. at 1070 . We held, among other things, that the arbitration agreement at issue could not “prohibit — i.e., require arbitration of — judicial actions seeking such public injunctive relief.” Id. at 1082 . To the extent it did so, the agreement was unenforceable. Id. We did not, however, analyze whether that rule contravened the FAA.

As prior circuit authority, Davis is controlling absent any clearly irreconcilable intervening higher authority. See Miller v. Gammie, 335 F.3d 889, 893 (9th Cir.2003) (en banc) (“[Wjhere the reasoning or theory of our prior circuit authority is clearly irreconcilable with the reasoning or theory of intervening higher authority, a three judge panel should consider itself bound by the later and controlling authority, and should reject the prior circuit opinion as having been effectively overruled.”); see also Rodriguez v. AT & T Mobility Servs. LLC, 728 F.3d 975, 978-80 (9th Cir.2013). We conclude that the portion of Davis applying the Broughton-Cruz rule is clearly irreconcilable with subsequent United States Supreme Court decisions concerning the FAA.

C. Preemption by the Federal Arbitration Act

We turn first to AT&T Mobility LLC v. Concepcion, — U.S.-, 131 S.Ct. 1740 , 179 L.Ed.2d 742 (2011). In Concepcion, the Supreme Court held that the FAA preempted a California rule — known as the Discover Bank rule — which invalidated most class action waivers in adhesion contracts, including arbitration agreements, as unconscionable. Id. at 1746, 1753. Of particular significance to this case is the Court’s statement that “[w]hen state law prohibits outright the arbitration of a particular type of claim, the analysis is straightforward: The conflicting rule is displaced by the FAA.” Id. at 1747.

This principle was reiterated in Marmet Health Care Center, Inc. v. Brown, — U.S.-, 132 S.Ct. 1201 , 182 L.Ed.2d 42 (2012) (per curiam), one of the decisions handed down after the district court’s order in this case. Marmet involved a West Virginia rule that invalidated any predispute agreement to arbitrate a personal injury or wrongful death claim against a nursing home. Id. at 1202 . That rule arose from three state-court negligence lawsuits each alleging the wrongful death of a nursing home patient. Id. In a decision concerning all three cases, the West Virginia Supreme Court of Appeals had held that “Congress did not intend for the FAA to be, in any way, applicable” to those particular types of lawsuits, as they only “collaterally derive” from a contract and “involve[ ] a service that is a practical necessity for members of the public.’’ Brown ex rel. Brown v. Genesis Healthcare Corp., 228 W.Va. 646 , 724 S.E.2d 250, 291 (2011), vacated sub nom., Marmet, 132 S.Ct. 1201 . The United States Supreme Court held the West Virginia court’s interpretation of the FAA to be “both incorrect and inconsistent with clear instruction” in its precedent. Marmet, 132 S.Ct. at 1203 . It stated: “As this Court reaffirmed last Term, ‘[wjhen state law prohibits outright the arbitration of a particular type of claim, the analysis is straightforward: The conflicting rule is displaced by the FAA.’ That rule resolves these cases.” Id. (alteration in Marmet) (quoting Concepcion, 131 S.Ct. at 1747).

That rule also resolves this case. By exempting from arbitration claims for public injunctive relief under the CLRA, UCL, and FAL, the Broughton-Cruz rule similarly prohibits outright arbitration of a particular type of claim.

We reject the argument that because an injunction is technically a remedy rather than a cause of action, the BroughtonCruz rule is insulated from the FAA. We do not think the Supreme Court intended such a technical reading of the word “claim.” As we have recognized en banc, recent Supreme Court decisions “have given broad effect to arbitration agreements.” Kilgore, 718 F.3d at 1057 . Just a few months ago, the Supreme Court reiterated that “courts must ‘rigorously enforce’ arbitration agreements according to their terms.” Am. Express Co. v. Italian Colors Rest., — U.S.-, 133 S.Ct. 2304, 2309 , 186 L.Ed.2d 417 (2013) (quoting Dean Witter Reynolds Inc. v. Byrd, 470 U.S. 213, 221 , 105 S.Ct. 1238 , 84 L.Ed.2d 158 (1985)).

Indeed, this argument appears to be foreclosed by Mastrobuono v. Shearson Lehman Hutton, Inc., 514 U.S. 52 , 115 S.Ct. 1212 , 131 L.Ed.2d 76 (1995). In Mastrobuono, 514 U.S. at 63-64, 66 , 115 S.Ct. 1212 , the Supreme Court found that a contract including an arbitration agreement and indicating that it was “governed by the laws of the State of New York” did not incorporate New York’s rule prohibiting punitive damages awards in arbitration. The New York rule was premised upon the New York Court of Appeals’ conclusion that punitive damages is a “social exemplary ‘remedy’ ” to address “public penal wrongs” that evoked “strong public policy” concerns precluding its application in a purely private setting. Garrity v. Lyle Stuart, Inc., 40 N.Y.2d 354 , 386 N.Y.S.2d 831 , 353 N.E.2d 793, 795-96 (1976). In rejecting the argument that the arbitration agreement incorporated the rule, the Supreme Court accepted the premise that the rule would be preempted in the absence of an agreement that incorporated it. See Mastrobuono, 514 U.S. at 58 , 115 S.Ct. 1212 (indicating that the Court’s prior decisions “make clear that if contracting parties agree to include claims for punitive damages within the issues to be arbitrated, the FAA ensures that their agreement will be enforced according to its terms even if a rule of state law would otherwise exclude such claims from arbitration”). The Supreme Court has since stated that Mastrobuono stands for the proposition that the “FAA pre-empts state law[s] requiring judicial resolution of claims involving punitive damages.” Marmet, 132 S.Ct. at 1204 (citing Mastrobuono, 514 U.S. at 56 , 115 S.Ct. 1212 ). Moreover, a rule that precludes an arbitrator from fashioning injunctive relief is similar to the Supreme Court’s illustrative list of preempted state rules in Concepcion, 131 S.Ct. at 1747. These include rules that would prohibit enforcement of arbitration agreements that failed to provide for “judicially monitored discovery,” “fail[ed] to abide by the Federal Rules of Evidence,” or “disallowed] an ultimate disposition by a jury.” Id. This all strongly suggests even where a specific remedy has implications for the public at large, it must be arbitrated under the FAA if the parties have agreed to arbitrate it.

Moreover, in applying the BroughtonCruz rule, the district court in this case apparently intended to determine for itself in the first instance whether Corinthian was liable under the UCL, FAL, and CLRA, and then, if it found liability, to consider whether an injunction was warranted. Under those circumstances, the effect of the Broughton-Cruz rule is to prohibit outright arbitration of three particular types of claims, so long as the plaintiff seeks a public injunction under those causes of action. This violates the FAA.

Subsequent decisions of the United States Supreme Court have made clear that the Broughton-Cruz rule is flawed in other ways as well. To begin with, the California Supreme Court relied on the inherent conflict analysis drawn from Mitsubishi Motors Corp. v. Soler Chrysler-Plymouth, Inc., 473 U.S. 614, 627-28 , 105 S.Ct. 3346 , 87 L.Ed.2d 444 (1985), but, as observed in the Italian Colors dissent, that analysis does not apply to state statutes such as those that form the basis of Plaintiffs’ request for a public injunction in this case. The “effective vindication” exception, which permits the invalidation of an arbitration agreement when arbitration would prevent the “effective vindication” of a federal statute, does not extend to state statutes. See Italian Colors, 133 S.Ct. at 2320 (Kagan, J., dissenting).

The effective vindication and inherent conflict exceptions are two sides of the same coin—the former turning on the ability to vindicate a statute, and the latter turning on the underlying purposes of a statute. Both exceptions are reserved for claims brought under federal statutes. They rest on the principle that other federal statutes stand on equal footing with the FAA. In both Mitsubishi Motors and Italian Colors the claims at issue were under the federal antitrust laws, and the argument was that the federal antitrust statutes modified the FAA. “In [the] all-federal context, one law does not automatically bow to the other.” Id. In contrast, as bluntly stated by Justice Kagan in her dissent in Italian Colors, “We have no earthly interest (quite the contrary) in vindicating” a state law. Id. Plaintiffs in this case, like the plaintiffs in the Broughton and Cruz cases, are pursuing state statutory claims.

The Italian Colors majority would agree with Justice Kagan’s dissent on this point. The central premise of the Supremacy Clause is that federal law is superior to state law. U.S. Const. art. VI, cl. 2. (“[T]he Laws of the United States ... shall be the supreme Law of the Land.”). The Supreme Court has therefore long recognized that any state law that “stands as an obstacle to the accomplishment and execution of the full purposes and objectives of Congress” is preempted. Hines v. Davidowitz, 312 U.S. 52, 67 , 61 S.Ct. 399 , 85 L.Ed. 581 (1941); see also Mortensen v. Bresnan Commc’ns, LLC, 722 F.3d 1151, 1157 (9th Cir.2013).

There is no reason to think that this principle does not apply to state rules that conflict with the FAA. “When a state rule allegedly conflicts with the FAA, we apply standard preemption principles, asking whether the state law frustrates the FAA’s purposes and objectives. If the state rule does so ... the Supremacy Clause requires its invalidation.” Italian Colors, 133 S.Ct. at 2320 (Kagan, J., dissenting). That there may be an inherent conflict is irrelevant. Cf. Nitro-Lift Technologies, LLC v. Howard, — U.S. -, 133 S.Ct. 500, 504 , 184 L.Ed.2d 328 (2012) (per curiam) (rejecting the argument that the FAA did not preempt an Oklahoma statute because that statute was more specific than the FAA, and explaining that the “interpretive principle that the specific governs the general ... applies only to conflict between laws of equivalent dignity,” but when a specific state statute conflicts with a general federal law, “the latter governs”).

The California Supreme Court’s reliance in Broughton, 90 Cal.Rptr.2d 334 , 988 P.2d at 77 , on the institutional advantages of the judicial forum is also inconsistent with AT&T Mobility LLC v. Concepcion. In Concepcion, 131 S.Ct. at 1747, the United States Supreme Court explained that state rules prohibiting enforcement of arbitration agreements that fail to provide for the judicial advantages of monitored discovery, evidence rules, or disposition by a jury would be impermissible under the FAA, as such rules disfavor arbitration. Simply put, “States cannot require a procedure that is inconsistent with the FAA, even if it is desirable for unrelated reasons.” Id. at 1753.

Moreover, in creating the Broughton^Cruz rule, the California court was motivated by its conclusion that the public injunction sought by the plaintiffs was “beyond the arbitrator’s power to grant.” Broughton, 90 Cal.Rptr.2d 334 , 988 P.2d at 76 . But that premise is not necessarily true. Corinthian concedes, and we agree, that an arbitrator generally has the authority to enter injunctive relief against a party that has entered into an arbitration agreement. Corinthian’s caveat, however, is that an arbitrator may do so only if the arbitration agreement at issue permits it. Whether, in this case, Plaintiffs’ arbitration agreements do so will need to be determined by the arbitrator. See Coast Trading Co. v. Pac. Molasses Co., 681 F.2d 1195, 1197-98 (9th Cir.1982) (describing an arbitrator’s role as the “interpretation and application of the parties’ agreement,” and stating that its award is “legitimate only so long as it draws its essence from the ... agreement” (alteration in Coast Trading) (quoting United Steelworkers of Am. v. Enter. Wheel & Car Corp., 363 U.S. 593, 597 , 80 S.Ct. 1358 , 4 L.Ed.2d 1424 (1960))).

We decline to resolve in advance the question of what, if any, court remedy Plaintiffs might be entitled to should the arbitrator determine that it lacks the authority to issue the requested injunction. That is beyond the scope of this appeal. If the arbitrator comes to that conclusion, Plaintiffs may return to the district court to seek their public injunctive relief. We express no opinion on any question that might arise at that time. Similarly, we decline to resolve now questions that could arise if a motion is brought in court to confirm an arbitration award that includes injunctive relief, or whether it might be necessary for a court to enforce a public injunction awarded by an arbitrator. Those questions can be better addressed in the context of an actual case, with arguments directed more specifically to the questions raised in that case.

We therefore hold that the FAA preempts the Broughton-Cruz rule. To the extent Davis v. O'Melveny & Myers, 485 F.3d 1066 (9th Cir.2007), held otherwise, it is clearly irreconcilable with intervening Supreme Court authority and has been overruled.

D. Plaintiffs’ Claims Are Within the Scope of Their Arbitration Agreements

Plaintiffs argue in the alternative that they should not be required to arbitrate their public injunction claims because those claims do not fall within the scope of their arbitration agreements. We disagree.

We first reject Corinthian’s attempt to characterize Plaintiffs’ argument as an improper cross-appeal. Because the district court rejected Plaintiffs’ scope argument in the section of its order compelling arbitration, Corinthian takes the position that Plaintiffs’ argument should be treated as a separate appeal that is both untimely and in violation of the FAA, which precludes the appeal of an order compelling arbitration. See 9 U.S.C. § 16 (b)(2) (“[A]n appeal may not be taken from an interlocutory order ... directing arbitration to proceed under section 4 of this title.”). But Plaintiffs are not asking us to reverse the ruling compelling arbitration. Rather, they have raised their scope argument as an alternative ground on which the panel may affirm the district court. They are entitled to do so. See, e.g., Atel Fin. Corp. v. Quaker Coal Co., 321 F.3d 924, 926 (9th Cir.2003) (per curiam).

Turning to the merits of Plaintiffs’ argument, because the scope of an arbitration agreement is a matter of con tract, we must look to the express terms of the agreements at issue to determine whether Plaintiffs and Corinthian intended that public injunction claims be arbitrated. See Chiron Corp. v. Ortho Diagnostic Sys., Inc., 207 F.3d 1126, 1130 (9th Cir.2000). Keeping in mind that “any doubts concerning the scope of arbitrable issues should be resolved in favor of arbitration,” we conclude that Plaintiffs’ claims do fall within the scope of their arbitration agreements. Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24-25 , 103 S.Ct. 927 , 74 L.Ed.2d 765 (1983).

Plaintiff Ferguson’s enrollment agreement states: “I understand that both I and The School are irrevocably waiving rights to a trial by jury, and are selecting instead to submit any and all claims to the decision of an arbitrator instead of a court.” His “Enrollment Agreement Addendum” further states: “I agree that any dispute arising from my enrollment, no matter how described, pleaded or styled, shall be resolved by binding arbitration under the Federal Arbitration Act.” Each of Plaintiff Muniz’s enrollment agreements provides: “Any dispute arising from enrollment at Heald College, no matter how described, pleaded or styled, shall be resolved by binding arbitration.” And her separate “Agreement to Binding Arbitration and Waiver of Jury Trial” states: “I, Sandra L. Muniz agree that any dispute arising from my enrollment at Heald College ... no matter how described, pleaded or styled, shall be resolved by binding arbitration.” Those terms are sufficiently broad to cover Plaintiffs’ public injunction claims.

Plaintiffs’ reliance on Tracer Research Corp. v. National Environmental Services Co., 42 F.3d 1292 (9th Cir.1994), is misplaced. Although Plaintiffs correctly point out that in Tracer Research we narrowly interpreted the phrase “arising under the Agreement” as covering only contract disputes related to the agreement itself, id. at 1295 , the terms in Plaintiffs’ agreements are broader than that, as they refer to “any disputes,” “all claims,” and disputes “arising from my enrollment.”

Plaintiffs’ argument that their public injunction claims are collateral to, rather than arising from, their enrollment because they pertain to recruiting is no more persuasive. Plaintiffs’ central complaint in this lawsuit is that Corinthian misrepresented the value and cost of an education at Heald and Everest schools. That complaint is directly related to enrollment.

III. Conclusion

The FAA preempts California’s Broughtonr-Cruz rule that claims for public injunctive relief cannot be arbitrated. We therefore reverse and remand the district court’s order denying Corinthian’s motion to compel arbitration of Plaintiffs’ claims for public injunctive relief. The district court is directed to grant the motion as to all claims, including Plaintiffs’ injunctive relief claims, and to stay the lawsuit pending arbitration.

In the event that the arbitrator concludes that Corinthian has violated the UCL, FAL, or CLRA, and that entry of an injunction might be appropriate, but further determines that it lacks the authority under the agreements at issue to grant the requested injunction, Plaintiffs may seek the requested injunction in court. We express no opinion about the merits of such action.

REVERSED and REMANDED.

. We reject Corinthian’s contention that Davis's application of the Broughton-Cruz rule was dicta and therefore non-binding. That we ultimately reached the same conclusion on a "more important[]” ground makes our ruling one in the alternative rather than dicta. See Davis, 485 F.3d at 1082-83 . Moreover, we explained en banc in Kilgore v. KeyBank, National Ass'n, 718 F.3d 1052, 1055 (9th Cir.2013), that the Broughton-Cruz rule was "recognized” in Davis . . Only this portion of our decision in Davis has been superseded. The portions not affect ed by the later United States Supreme Court decisions remain valid precedent. . Corinthian's argument that the FAA preempts the Broughton-Cruz rule was raised by the appellants in Kilgore . On rehearing en banc, we did not reach the appellants’ argument, however, because we concluded that the injunction sought was not a public injunction. Kilgore, 718 F.3d at 1060-61 . It would have benefitted only the class members, as it "relate[d] only to past harms suffered by the members of the limited putative class,” not the general public. Id. at 1061 . By contrast, Plaintiffs in this case seek to enjoin Corinthian from continuing to engage in a purported scheme to entice prospective students through misrepresentations. Such an injunction would have no benefit for Plaintiffs, as they have already enrolled in Corinthian's schools, but may prevent others from enrolling in a Corinthian school based on any misrepresentations.