a)
2^{-5}=(\frac{1}{2})^5=\frac{1}{32}
b)
(-2\frac{1}{2})^{-2}=(-\frac{5}{2})^{-2}=(-\frac{2}{5})^2=\frac{4}{25}=0,16
c)
16^{\frac{1}{4}}=(2^4)^{\frac{1}{4}}=2
e)
(\frac{8}{27})^{-\frac{2}{3}}=((\frac{2}{3})^3)^{-\frac{2}{3}}=(\frac{2}{3})^{-2}=(\frac{3}{2})^2=\frac{9}{4}=2\frac{1}{4}=2,25
e)
3^{10}\cdot (3^3)^{-4}=3^{10}\cdot 3^{-12}=3^{-2}
f)
(5^{-4})^5:5^{-18}=5^{-20-18}=5^{-38}
g)
{\frac{\sqrt[3]2}{\sqrt2}\cdot 2^{\frac{7}{6}}=\frac{2^{\frac{1}{3}}\cdot 2^{\frac{7}{6}}}{\sqrt2}=\frac{2^{\frac{2}{6}+\frac{7}{6}}}{2^{\frac{1}{2}}}=\frac{2^{\frac{9}{6}}}{2^{\frac{3}{6}}}=2^{\frac{9-3}{6}}=2^{\frac{6}{6}}=2^1=2}
h)
64^{-\frac{1}{2}}\cdot 8^{\frac{5}{3}}=(2^6)^{-\frac{1}{2}}\cdot (2^3)^{\frac{5}{3}}=2^{-3}\cdot 2^5=2^2=4
i)
{(9^{\frac{1}{3}}\cdot 9^{\frac{1}{3}}):9^{\frac{1}{12}}=9^{\frac{2}{3}}:9^{\frac{1}{12}}=(3^2)^{\frac{2}{3}}:(3^2)^{\frac{1}{12}}=3^{\frac{4}{3}}:3^{\frac{1}{6}}=3^{\frac{8}{6}-\frac{1}{6}}=3^{\frac{7}{6}}=3^{\frac{6}{6}} \cdot 3^{\frac{1}{6}}=3\sqrt[6]{3}}