Chapter 13.2, Problem 46E

To determine

To evaluate: The expression $2^{x-1}$ if $x^2=36$ .

Answer to Problem 46E

The correct option is (E).

Explanation of Solution

Given:

It is given that $x^2=36$ .

Calculation:

Simplify the equation $x^2=36$ .

  $\begin{array}{c}{x}^2=36\\ x=\sqrt{36}\\ =\pm 6\end{array}$

Substitute 6 for $x$ in the expression $2^{x-1}$ .

  $\begin{array}{c}{2}^{x-1}=2^{6-1}\\ =2^5\\ =32\end{array}$

Substitute $-6$ for $x$ in the expression $2^{x-1}$ .

  $\begin{array}{c}{2}^{x-1}=2^{-6-1}\\ =2^{-7}\\ =\frac{1}{128}\end{array}$

Therefore, the correct option is (E).