The correct solution in simplifying the given mathematical expression is [tex]-\frac{25}{x^3}[/tex].
Given the following data:
To determine the correct solution in simplifying the given mathematical expression:
In this scenario, you're required to simplify the given mathematical expression in its simplest form.
Step 1: We would apply the basic law of division for fractions.
[tex](-5^{-2}x^3)^{-1}=(\frac{-1}{5^2} \times x^3)^{-1}\\\\[/tex]
Step 2: We would expand the bracket.
[tex](\frac{-1}{5^2} \times x^3)^{-1}=(\frac{-x^3}{5^2} )^{-1}\\\\(\frac{-x^3}{5^2} )^{-1}=(\frac{-x^3}{25} )^{-1}\\\\[/tex]
Step 3: We would apply the inverse of fraction.
[tex](\frac{-x^3}{25} )^{-1}= -\frac{25}{x^3}[/tex]
Read more on law of division here: https://brainly.com/question/19660239
