Charcoal, 9 bytes

ＩΣＥ⊕ηＸＩθι

Try it online! Link is to verbose version of code. Explanation:

    η       Second input
   ⊕        Increment
  Ｅ         Map over implicit range
        ι   Current index
       θ    First input
      Ｉ     Cast to number
     Ｘ      Power
 Σ          Sum
Ｉ           Cast to string
            Implicitly print

Unfortunately Power doesn't vectorise otherwise the answer would be 8 bytes:

       Ｎ    Second input as a number
      ⁰     Literal 0
    …·      Inclusive range
   Ｎ        First input as a number
  Ｘ         Power
 Σ          Sum
Ｉ           Cast to string
            Implicitly print

Charcoal, 9 7 bytes

Ｉ↨ＮＥ⊕Ｎ¹

Try it online! Link is to verbose version of code. Uses @Bubbler's algorithm. Explanation:

     Ｎ  Second input as a number
    ⊕   Increment
   Ｅ  ¹ Make list of `1`s of that length
  Ｎ     First input as a number
 ↨      Base conversion
Ｉ       Cast to string
        Implicitly print