Question

For what integer $n$ is $(0. 125)^4$ equal to $2^n$?

Answer 1

n=-12

Step-by-step explanation:

0.125 = 1/8

2^3 = 8

1/(2^3) = 1/8

2^(-3) = 1/8

2^(-3) = 0.125

(0.125)^4 = (2^(-3))^4

(0.125)^4 = 2^(-3(4))

(0.125)^4 = 2^(-12)

Hence, n=-12