Question

What option is the same as 1/5^-3? A. -1/125 B. -1/15 C. 15 D. 125

Answer 1

Answer:

D. 125

Step-by-step explanation:

Given

$(\frac{1}{5})^{-3}$

Required

Find Equivalent

From law of indices

$(\frac{1}{a})^{-x} = \frac{1}{(\frac{1}{a})^{x}}$

So,

$(\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})^{3}}$

Expand denominator

$(\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})*(\frac{1}{5})*(\frac{1}{5})}}$

$(\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{125})}}$

Split expression on the right and side

$(\frac{1}{5})^{-3} = 1/{(\frac{1}{125})}}$

Convert divide (/) to multiplication (*)

$(\frac{1}{5})^{-3} = 1*{(\frac{125}{1})}}$

$(\frac{1}{5})^{-3} = 1*125$

$(\frac{1}{5})^{-3} = 125$

Hence, $(\frac{1}{5})^{-3}$ is equivalent to 125