AMC12 2015 B

AMC12 2015 B · Q8

AMC12 2015 B · Q8. It mainly tests Exponents & radicals.

What is the value of $\left(625^{\log_5 2015}\right)^{\frac{1}{4}}$?

$\left(625^{\log_5 2015}\right)^{\frac{1}{4}}$ 的值是多少？

(A) 5 5

(B) $\sqrt[4]{2015}$ $\sqrt[4]{2015}$

(D) 2015 2015

(E) $\sqrt[4]{5^{2015}}$ $\sqrt[4]{5^{2015}}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): $(625^{\log_5 2015})^{\frac{1}{4}}=((5^4)^{\log_5 2015})^{\frac{1}{4}}=(5^{4\log_5 2015})^{\frac{1}{4}}=(5^{\log_5 2015})^{4\cdot\frac{1}{4}}=2015$

答案（D）： $(625^{\log_5 2015})^{\frac{1}{4}}=((5^4)^{\log_5 2015})^{\frac{1}{4}}=(5^{4\log_5 2015})^{\frac{1}{4}}=(5^{\log_5 2015})^{4\cdot\frac{1}{4}}=2015$

Topics

AL.008 Exponents & radicals