Answer:
D. 125
Step-by-step explanation:
Given
[tex](\frac{1}{5})^{-3}[/tex]
Required
Find Equivalent
From law of indices
[tex](\frac{1}{a})^{-x} = \frac{1}{(\frac{1}{a})^{x}}[/tex]
So,
[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})^{3}}[/tex]
Expand denominator
[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{5})*(\frac{1}{5})*(\frac{1}{5})}}[/tex]
[tex](\frac{1}{5})^{-3} = \frac{1}{(\frac{1}{125})}}[/tex]
Split expression on the right and side
[tex](\frac{1}{5})^{-3} = 1/{(\frac{1}{125})}}[/tex]
Convert divide (/) to multiplication (*)
[tex](\frac{1}{5})^{-3} = 1*{(\frac{125}{1})}}[/tex]
[tex](\frac{1}{5})^{-3} = 1*125[/tex]
[tex](\frac{1}{5})^{-3} = 125[/tex]
Hence, [tex](\frac{1}{5})^{-3}[/tex] is equivalent to 125
