Q38. - Algebra 2

Question

Simplify  ${\left(\frac{x}{y^{-1}}\right)}^{-2}$ assuming that no variable equal to 0 .

Step-by-Step Solution

Answer

The simplified value of expression is $\frac{1}{x^2{y}^2}$ .

Step 1. Write down the given expression.

The given expression to simplify is ${\left(\frac{x}{y^{-1}}\right)}^{-2}$ .

Step 2. Simplify the given expression.

Simplifying ${\left(\frac{x}{y^{-1}}\right)}^{-2}$  gives,

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

Step 3. Conclusion.

The simplified value of expression is $\frac{1}{x^2{y}^2}$ .