## Algebra 2 (1st Edition)

We know the following rules of exponents. The list of names is on page 330. $$(1) \ a^m\cdot a^n = a^{m+n} \\ (2) \ (ab)^m =a^mb^m \\ (3) \ (a^m)^n =a^{mn} \\ (4) \ a^{-m} = \frac{1}{a^m} \\ (5)\ \frac{a^m}{a^n} =a^{m-n} \\ (6) \ a^0=1 \\ (7) \ (\frac{a}{b})^m =\frac{a^m}{b^m}$$ Thus, using the negative exponent and quotient of powers properties: $$=5^{-3}=\frac{1}{5^3}=\frac{1}{125}$$