Question

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

Answer 1

D. 125

Explanation:

Given

`((1)/(5))^(-3)`

Required

Find Equivalent

From law of indices

`((1)/(a))^(-x) = (1)/(((1)/(a))^(x))`

So,

`((1)/(5))^(-3) = (1)/(((1)/(5))^(3))`

Expand denominator

`((1)/(5))^(-3) = (1)/(((1)/(5))*((1)/(5))*((1)/(5)))}`

`((1)/(5))^(-3) = (1)/(((1)/(125)))}`

Split expression on the right and side

`((1)/(5))^(-3) = 1/{((1)/(125))}}`

Convert divide (/) to multiplication (*)

`((1)/(5))^(-3) = 1*{((125)/(1))}}`

`((1)/(5))^(-3) = 1*125`

`((1)/(5))^(-3) = 125`

Hence,
`((1)/(5))^(-3)` is equivalent to 125