What is the value of (625^_5 2015)^14 ?

(625^_5 2015)^14 = ((5^4)^_5 2015)^14 = (5^4 _5 2015)^14 = (5^_5 2015 4)^14 = ((5^_5 2015)^4)^14 = (2015^4)^14 = 2015

smc

algebra senior

Problem

What is the value of

(62 5^{l o g_{5} 2015})^{\frac{1}{4}}

(A)

5

(B)

42015

(C)

625

(D)

2015

Solution

(62 5^{l o g_{5} 2015})^{\frac{1}{4}} = ((5^{4})^{l o g_{5} 2015})^{\frac{1}{4}} = (5^{4 \cdot l o g_{5} 2015})^{\frac{1}{4}} = (5^{l o g_{5} 2015 \cdot 4})^{\frac{1}{4}} = ((5^{l o g_{5} 2015})^{4})^{\frac{1}{4}} = (201 5^{4})^{\frac{1}{4}} = 2015

Final answer