Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises - Page 437: 24

$t=2$

$(\frac{1}{3})^{t}=\frac{1}{9}$ $(\frac{1}{3})^{t}=\frac{1^{2}}{3^{2}}$ $(\frac{1}{3})^{t}=(\frac{1}{3})^{2}$ $t=2$ Check: $(\frac{1}{3})^{2}\overset{?}{=}\frac{1}{9}$ $\frac{1^{2}}{3^{2}}\overset{?}{=}\frac{1}{9}$ $\frac{1}{9}=\frac{1}{9}$.