The expression which is equivalent to the provided expression of variable x is,
![\dfrac{1}{1000x^3}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B1000x%5E3%7D)
<h3>What is the equivalent expression?</h3>
Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given expression in the problem is,
![(10x)-3](https://tex.z-dn.net/?f=%2810x%29-3)
Let the equivalent expression of this expression is f(<em>x)</em>. Thus,
![f(x)=(10x)^{-3}](https://tex.z-dn.net/?f=f%28x%29%3D%2810x%29%5E%7B-3%7D)
The number, with negative power, can be written in the fraction of 1 with the same but positive power or exponent. Therefore,
![f(x)=\dfrac{1}{(10x)^{3}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7B%2810x%29%5E%7B3%7D%7D)
Solve it further as,
![f(x)=\dfrac{1}{(10)^3(x)^{3}}\\f(x)=\dfrac{1}{1000x^3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7B%2810%29%5E3%28x%29%5E%7B3%7D%7D%5C%5Cf%28x%29%3D%5Cdfrac%7B1%7D%7B1000x%5E3%7D)
Hence, the expression which is equivalent to the provided expression of variable x is,
![\dfrac{1}{1000x^3}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B1000x%5E3%7D)
Learn more about the equivalent expression here;
brainly.com/question/2972832