Question

Simplify${\left(\frac{-6x^6}{3x^3}\right)}^{-2}$ assuming that no variable equal to 0 .

Short answer

The simplified value of expression is $\frac{1}{4x^6}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression to simplify is ${\left(\frac{-6x^6}{3x^3}\right)}^{-2}$.

Step 2. Simplify the given expression.

Simplifying ${\left(\frac{-6x^6}{3x^3}\right)}^{-2}$ gives,

$\begin{array}{c}{\left(\frac{-6x^6}{3x^3}\right)}^{-2}={(-\frac{3x^3}{6x^6})}^2\\ ={(-\frac{x^3}{2x^6})}^2\\ ={(-\frac{1}{2})}^2{\left(x^{3-6}\right)}^2\\ =\frac{{\left(x^{-3}\right)}^2}{4}\\ =\frac{x^{-6}}{4}\\ =\frac{1}{4x^6}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{1}{4x^6}$.