# [Jelly], <s>12</s> 11 bytes

    1*@ṾØDfƑʋ1#

[Try it online!][TIO-jpvx4wof]

### How it works

    1*@ṾØDfƑʋ1#  Main link. Argument: n

    1            Set the return value to 1.
             1#  Call the link to the left for k = 1, 2, ... and with right argument n,
                 until it returns a truthy value.
            ʋ      Combine the four links to the left into a dyadic chain.
     *@              Compute n**k.
       Ṿ             Convert it to its string representation.
        ØD           Yield "0123456789".
          fƑ         Filter and return 1 is the result is equal to the left argument.

[Jelly]: https://github.com/DennisMitchell/jelly
[TIO-jpvx4wof]: https://tio.run/##AUEAvv9qZWxsef//MSpA4bm@w5hEZsaRyosxI/8yIHIgMzYg4bifIDEwIDsgMTIzNDU2Nzg5MCDCtSA7IiDDh@KCrCBH/w "Jelly – Try It Online"