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edited Mar 19, 2018 at 11:23

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Brachylog, 12 bytes

{^a₀.&b~b^}ᶜ

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Explanation

{^a₀.&b~b^}ᶜ
{         }ᶜ  Count the number of ways the following can succeed:
  a₀            A prefix of
 ^                the first {input} to the power of the second {input}
    .&          produces the same output with the same input as
       ~b         any number
         ^        to the power of
      b           all inputs but the lastfirst (i.e. the second input)

Brachylog, 12 bytes

{^a₀.&b~b^}ᶜ

Try it online!

Explanation

{^a₀.&b~b^}ᶜ
{         }ᶜ  Count the number of ways the following can succeed:
  a₀            A prefix of
 ^                the first {input} to the power of the second {input}
    .&          produces the same output with the same input as
       ~b         any number
         ^        to the power of
      b           all inputs but the last (i.e. the second input)

Brachylog, 12 bytes

{^a₀.&b~b^}ᶜ

Try it online!

Explanation

{^a₀.&b~b^}ᶜ
{         }ᶜ  Count the number of ways the following can succeed:
  a₀            A prefix of
 ^                the first {input} to the power of the second {input}
    .&          produces the same output with the same input as
       ~b         any number
         ^        to the power of
      b           all inputs but the first (i.e. the second input)

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created Mar 18, 2018 at 20:16

ais523

Brachylog, 12 bytes

{^a₀.&b~b^}ᶜ

Try it online!

Explanation

{^a₀.&b~b^}ᶜ
{         }ᶜ  Count the number of ways the following can succeed:
  a₀            A prefix of
 ^                the first {input} to the power of the second {input}
    .&          produces the same output with the same input as
       ~b         any number
         ^        to the power of
      b           all inputs but the last (i.e. the second input)