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Algebra Difficulty 2.1 Junior Find the answer

What is the value of (625log⁡52015)14(625^{\log_5 2015})^{\frac{1}{4}} ?

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Solution

(625log⁡52015)14=((54)log⁡52015)14=(54⋅log⁡52015)14=(5log⁡52015⋅4)14=((5log⁡52015)4)14=(20154)14=(D)  2015(625^{\log_5 2015})^\frac{1}{4} = ((5^4)^{\log_5 2015})^\frac{1}{4} = (5^{4 \cdot \log_5 2015})^\frac{1}{4} = (5^{\log_5 2015 \cdot 4})^\frac{1}{4} = ((5^{\log_5 2015})^4)^\frac{1}{4} = (2015^4)^\frac{1}{4} = \boxed{\textbf{(D)}\; 2015}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.