Q39. - Algebra 2

Question

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

Step-by-Step Solution

Answer

The simplified value of expression is $\frac{1}{v^3{w}^6}$ .

Step 1. Write down the given expression.

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

Step 2. Simplify the given expression.

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

$\begin{array}{c}{\left(\frac{v}{w^{-2}}\right)}^{-3}=\frac{{\left(v\right)}^{-3}}{{\left(w^{-2}\right)}^{-3}}\mathrm{....}(\text{Using }{\left(\frac{x}{y}\right)}^n=\frac{{\left(x\right)}^n}{{\left(y\right)}^n})\\ =\frac{v^{-3}}{w^6}\\ =\frac{1}{v^3{w}^6}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{1}{v^3{w}^6}$ .