a)
8^{-\frac{1}{3}}=(2^3)^{-\frac{1}{3}}=2^{-1}=\frac{1}{2}
27^{-\frac{4}{3}}=(3^3)^{-\frac{4}{3}}=3^{-4}=(\frac{1}{3})^4=\frac{1}{81}
64^{-\frac{1}{3}}=(4^3)^{-\frac{1}{3}}=4^{-1}=\frac{1}{4}
b)
(\frac{1}{16})^{-\frac{1}{2}}=16^{\frac{1}{2}}=\sqrt{16}=4
(\frac{1}{27})^{-\frac{2}{3}}=27^{\frac{2}{3}}=(3^3)^{\frac{2}{3}}=3^2=9
(\frac{16}{25})^{-\frac{3}{4}}=(\frac{25}{16})^{\frac{3}{4}}=((\frac{5}{4})^2)^{\frac{3}{4}}=(\frac{5}{4})^{\frac{3}{2}}=\sqrt{(\frac{5}{4})^3}=\frac{\sqrt{125}}{\sqrt{64}}=\frac{5\sqrt5}{8}