What is the value of (625^log_5 2015)^14?

2015 AMC 12B Problem 8

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What is the value of

\left(625^{\log_5 2015}\right)^{\frac14}?

5

\sqrt[4]{2015}

625

2015

\sqrt[4]{5^{2015}}

625 = 5^4

Use

5^{\log_5 x} = x

after collecting the exponents

Since

625 = 5^4,

we have

\begin{gathered} 625^{\log_5 2015} = 5^{4\log_5 2015} \\ = \left(5^{\log_5 2015}\right)^4 = 2015^4. \end{gathered}

Taking the fourth root gives

\left(2015^4\right)^{\frac{1}{4}} = 2015.

Thus, the correct answer is D.