Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 788: 77

$t^{13/15}$

Apply the rule $\qquad a^{m}a^{n}=a^{m+n}$ $t^{1/5}\cdot t^{2/3}=t^{\frac{1}{5}+\frac{2}{3}}=$ $\displaystyle \frac{1}{5}+\frac{2}{3}=$ ... (lcd = 15) ...$=\displaystyle \frac{3}{15}+\frac{10}{15}=\frac{13}{15}$ $...=t^{13/15}$