## Intermediate Algebra for College Students (7th Edition)

If $7^{-2}$ is raised to the third power, the result is a number between 0 and 1. --> The statement makes sense.
$7^{-2}$ is raised to the third power can be written as: $(7^{-2})^{3}$. Evaluate. Recall the power rule: $(a^{m})^{n}=a^{mn}$ Thus, $$(7^{-2})^{3} = 7^{-6}$$ Recall the negative exponent rule: $a^{−n}=\frac{1}{a^{n}}$ Thus, $$7^{-6} = \frac{1}{7^{6}}$$ $\frac{1}{7^{6}}$ is a number that lies between $0$ and $1$; hence, the statement makes sense.