#Jelly, 7 bytes (non-competing) D*DL$S⁼ Try it online!

Or alternatively (uses 2 chains):

Dµ*LS⁼Ḍ

Explanation of the first code:

 D* DL$S⁼  Main link (monadic). Arguments: z
⁸          (implicit) z
 D         List of digits of z
   ⁸       (implicit) z
    D      List of digits of z
     L     Length of z
      $    Last two links as a monad
  *        Exponentiation with base x and exponent y
       S   Sum of z
         ⁸ (implicit) z
        ⁼  Check if x equals y

Jelly, 7 bytes (non-competing)

D*DL$S⁼

Try it online!

Or alternatively (uses 2 chains):

Dµ*LS⁼Ḍ

Explanation of the first code:

 D* DL$S⁼  Main link (monadic). Arguments: z
⁸          (implicit) z
 D         List of digits of z
   ⁸       (implicit) z
    D      List of digits of z
     L     Length of z
      $    Last two links as a monad
  *        Exponentiation with base x and exponent y
       S   Sum of z
         ⁸ (implicit) z
        ⁼  Check if x equals y

#Jelly, 7 bytes (non-competing) D*DL$S⁼ Try it online!

Or alternatively (uses 2 chains):

Dµ*LS⁼Ḍ

Explanation of the

#Jelly, 7 bytes (non-competing) D*DL$S⁼ Try it online!

Or alternatively (uses 2 chains):

Dµ*LS⁼Ḍ

Explanation of the first code:

 D* DL$S⁼  Main link (monadic). Arguments: z
⁸          (implicit) z
 D         List of digits of z
   ⁸       (implicit) z
    D      List of digits of z
     L     Length of z
      $    Last two links as a monad
  *        Exponentiation with base x and exponent y
       S   Sum of z
         ⁸ (implicit) z
        ⁼  Check if x equals y