Answer
(a) $\frac{1}{x^{3}y^{3}}$
(b) $\frac{b^{6}}{a^{12}}$
(c) $\frac{8}{x^{10}y^{13}}$
Work Step by Step
(a) $(x^{3}y^{3})^{-1}=\frac{1}{x^{3}y^{3}}$
(b) $(a^{2}b^{-2})^{-3}(a^{3})^{-2}=a^{2(-3)}b^{-2(-3)}a^{3(-2)}=a^{-6}b^{6}a^{-6}=a^{-6+-6}b^{6}=\frac{b^{6}}{a^{12}}$
(c) $(\frac{x^{2}}{y^{-2}})^{-2}(\frac{2y^{-3}}{x^{2}})^{3}=x^{2(-2)}y^{-(-2)(-2)}\cdot 2^{3}y^{-3(3)}x^{-2(3)}=x^{-4}y^{-4} 8y^{-9}x^{-6}=8x^{-4-6}y^{-4-9}=\frac{8}{x^{10}y^{13}}$
