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-14 bytes thanks to UltimateHawk!
(define(f n)(let g([a n][bn[b 1])(if(= 10(length(remove-duplicates(string->list(~v(expt an b))))))b(gf an(+ b 1)))))
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(define(f n)(let g([a n][b 1])(if(= 10(length(remove-duplicates(string->list(~v(expt a b))))))b(g a(+ b 1)))))
Try it online!
(define(f n[b 1])(if(= 10(length(remove-duplicates(string->list(~v(expt n b))))))b(f n(+ b 1))))
