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

Answer:

$(\frac{x^{-6}}{x^2})^3 = \frac{1}{x^{24}}$

Step-by-step explanation:

Given

$(\frac{x^{-6}}{x^2})^3$

Required

Determine the equivalent expression

$(\frac{x^{-6}}{x^2})^3$

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

Apply the following law of indices:

$\frac{x^a}{x^b} = x^{a-b}$

So:

$(\frac{x^{-6}}{x^2})^3$ becomes

= $(x^{-6-2})^3$

= $(x^{-8})^3$

Open the bracket

= $x^{-8*3}$

= $x^{-24}$

Convert the above expression to fraction

= $\frac{1}{x^{24}}$

Hence:

$(\frac{x^{-6}}{x^2})^3 = \frac{1}{x^{24}}$

Answer 2

Answer:

D on edge 2020 1/x24

Step-by-step explanation: