Question

If (5^1/5)^5 = 25^x, then x = ?

Answer 1

Answer:

  x = 1/2

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

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  (5^(1/5))^5 = 25^x . . . . given

  5^(1/5×5) = (5^2)^x . . . . simplify left side, rewrite right side

  5^1 = 5^(2x) . . . . . . . . . simplify further

  1 = 2x . . . . . . . . . . . . . equate exponents of the same base

  x = 1/2 . . . . . . . . . . . divide by 2

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Additional comment

The Order of Operations tells you that exponentiation must be evaluated before multiplication or division. That means 5^1/5 is evaluated as ...

  (5^1)/5 = 5/5 = 1

If you want a fractional exponent, it must be put in parentheses: 5^(1/5). If you type your expression into the Go.ogle calculator, it will strictly adhere to the Order of Operations.