Chapter 7.9, Problem 14OE

To determine

To calculate: The simplified form of the expression ${\left(3^{-1}\right)}^{-2}$ .

Answer to Problem 14OE

The simplified form of the expression ${\left(3^{-1}\right)}^{-2}$ is $9$ .

Explanation of Solution

Given information:

The expression ${\left(3^{-1}\right)}^{-2}$ .

Formula used:

Law of exponent for power of power is ${\left(a^m\right)}^n=a^{mn}$ where a is a nonzero integers and n and m are positive integers.

Calculation:

Consider the expression ${\left(3^{-1}\right)}^{-2}$ .

Recall that law of exponent for power of power is ${\left(a^m\right)}^n=a^{mn}$ where a is a nonzero integers and n and m are positive integers.

Apply it,

  $\begin{array}{c}{\left(3^{-1}\right)}^{-2}=3^{\left(-1\right)\left(-2\right)}\\ =3^2\\ =9\end{array}$

Thus, the simplified form of the expression ${\left(3^{-1}\right)}^{-2}$ is $9$ .