Chapter 7.9, Problem 21OE

To determine

To calculate: The simplified form of the expression $a^{-1}{b}^2$ .

Answer to Problem 21OE

The simplified form of the expression $a^{-1}{b}^2$ is $\frac{b^2}{a}$ .

Explanation of Solution

Given information:

The expression $a^{-1}{b}^2$ .

Formula used:

The expression $a^{-n}$ is expressed as $\frac{1}{a^n}$ where a is a nonzero real number and n is a positive integer.

Calculation:

Consider the expression $a^{-1}{b}^2$ .

Recall that expression $a^{-n}$ is expressed as $\frac{1}{a^n}$ where a is a nonzero real number and n is a positive integer.

Apply it,

  $\begin{array}{c}{a}^{-1}{b}^2=a^{-1}\cdot b^2\\ =\frac{1}{a}\cdot b^2\\ =\frac{b^2}{a}\end{array}$

Thus, the simplified form of the expression $a^{-1}{b}^2$ is $\frac{b^2}{a}$ .