[tex](x^{-6}/x^{2} )^{3}[/tex] = [tex]1/x^{24}[/tex] is expression is equivalent to (start fraction x superscript negative 6 baselines over x squared end fraction) cubed.
Given:
[tex](x^{-6}/x^{2} )^{3}[/tex]
Determine the equivalent expression
[tex](x^{-6}/x^{2} )^{3}[/tex]
First, we need to evaluate the expression in the bracket:
Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.
So, apply the following law of indices:
[tex]w^{x} /w^{y} = w^{x-y}[/tex]
So,
[tex](x^{-6}/x^{2} )^{3}[/tex] becomes:
=> [tex]x^{(-6-2)^{3}[/tex]
=> [tex]x^ {(-8 )^{3}\\[/tex]
Again apply the following law of indices:
[tex](w^m)^n = w^m^n[/tex]
Open the bracket
=> [tex]x^{-8 * 3}[/tex]
=> [tex]x^{-24}[/tex]
Convert the above expression to a fraction:
= [tex]1/x^{24}[/tex]
Hence, [tex](x^{-6}/x^{2} )^{3}[/tex] = [tex]1/x^{24}[/tex]
To learn more about the law of indices: https://brainly.com/question/27432311
#SPJ4
