## Precalculus: Mathematics for Calculus, 7th Edition

a) $\frac{a^{19}b}{c^9}$ b) $\frac{v^{10}}{u^{11}}$
a) $($$\frac{a^2}{b}$$)$$^5$$($$\frac{a^3b^2}{c^3}$$)$$^3 = \frac{a^{(2)(5)}}{b^5}$$\frac{a^{(3)(3)}b^{(2)(3)}}{c^{(3)(3)}}$ = $\frac{a^{10+9}b^{6-5}}{c^9}$ = $\frac{a^{19}b}{c^9}$ b) $\frac{(u^{-1}v^2)^{2}}{(u^{3}v^{-2})^3}$ = $\frac{u^{(-2)(2)}v^{(2)(2)}}{u^{(3)(3)}v^{(-2)(3)}}$ = $u^{-4-9}$$v^{4+6} = u^{-11}$$v^{10}$ = $\frac{v^{10}}{u^{11}}$