Equivalent expression of [tex]x^{-4}[/tex] is simplified way of given expression, with avoiding the negative exponent. The expression which is equivalent to the given expression is,
[tex]\left ( \dfrac{1}{x} \right )^4[/tex]
What is equivalent expression?
Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.
Given information-
The expression given in the problem is,
[tex]x^{-4}[/tex]
Let the equivalent expression of the given expression is [tex]f(x)[/tex]. Thus,
[tex]f(x)=x^{-4}[/tex]
When the exponent of any number is negative, then it can be written in the denominator with the same exponent with positive sign. Thus,
[tex]f(x)=\dfrac{1}{x^{4}}[/tex]
As the any power of 1 is equal to the 1. Thus putting the power 4 over the number 1 does not affect the expression. Thus,
[tex]f(x)=\dfrac{1^4}{x^{4}}[/tex]
As both the numerator and denominator has the same power. Thus it can be written over the bracket as,
[tex]f(x)= \left ( \dfrac{1}{x} \right )^4[/tex]
Hence, the expression which is equivalent to the given expression is,
[tex]\left ( \dfrac{1}{x} \right )^4[/tex]
Learn more about the equivalent expression here;
https://brainly.com/question/2972832
