Question

Which expression is equivalent to (StartFraction x Superscript negative 6 Baseline Over x squared EndFraction) cubed? StartFraction 1 Over x EndFraction StartFraction 1 Over x Superscript 5 Baseline EndFraction StartFraction 1 Over x Superscript 9 Baseline EndFraction StartFraction 1 Over x Superscript 24 Baseline EndFraction

Answer 1

D on edge 2020 1/x24

Explanation:

Answer 2

`((x^(-6))/(x^2))^3 = (1)/(x^(24))`

Explanation:

Given

`((x^(-6))/(x^2))^3`

Required

Determine the equivalent expression

`((x^(-6))/(x^2))^3`

First, we need to evaluate the expression in the bracket:

Apply the following law of indices:

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

So:

`((x^(-6))/(x^2))^3` becomes

=
`(x^(-6-2))^3`

=
`(x^(-8))^3`

Open the bracket

=
`x^(-8*3)`

=
`x^(-24)`

Convert the above expression to fraction

=
`(1)/(x^(24))`

Hence:

`((x^(-6))/(x^2))^3 = (1)/(x^(24))`