Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 437: 23

$x=4$

$(\frac{1}{2})^{x}=\frac{1}{16}$ $(\frac{1}{2})^{x}=\frac{1^{4}}{2^{4}}$ $(\frac{1}{2})^{x}=(\frac{1}{2})^{4}$ $x=4$ Check: $(\frac{1}{2})^{4}\overset{?}{=}\frac{1}{16}$ $\frac{1^{4}}{2^{4}}\overset{?}{=}\frac{1}{16}$ $\frac{1}{16}=\frac{1}{16}$.