Answer:
[tex](\frac{x^{-6}}{x^2})^3 = \frac{1}{x^{24}}[/tex]
Step-by-step explanation:
Given
[tex](\frac{x^{-6}}{x^2})^3[/tex]
Required
Determine the equivalent expression
[tex](\frac{x^{-6}}{x^2})^3[/tex]
First, we need to evaluate the expression in the bracket:
Apply the following law of indices:
[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]
So:
[tex](\frac{x^{-6}}{x^2})^3[/tex] becomes
= [tex](x^{-6-2})^3[/tex]
= [tex](x^{-8})^3[/tex]
Open the bracket
= [tex]x^{-8*3}[/tex]
= [tex]x^{-24}[/tex]
Convert the above expression to fraction
= [tex]\frac{1}{x^{24}}[/tex]
Hence:
[tex](\frac{x^{-6}}{x^2})^3 = \frac{1}{x^{24}}[/tex]
