a)

${\left(3^{-2}\right)}^2=3^{-4}={\left(\frac{1}{3}\right)}^4=\frac{1}{81}$  

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b) 

${\left(\frac{1}{2}\right)}^{-4}=2^4=16$  

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c)

$2^{-3}\cdot {\left(\frac{1}{2}\right)}^{-3}={\left(2\cdot \frac{1}{2}\right)}^{-3}=1^{-3}=1^3=1$

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d)

$9^3\cdot 3^{-5}={\left(3^2\right)}^3\cdot 3^{-5}=3^6\cdot 3^{-5}=3^1=3$  

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e)

$\frac{2^{-3}\cdot 4^{-2}}{2^{-6}}=\frac{2^{-3}\cdot 2^{-4}}{2^{-6}}=\frac{2^{-7}}{2^{-6}}=2^{-1}=\frac{1}{2}$  

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f)

$\frac{{10}^{-2}}{5^{-6}\cdot {25}^2}=\frac{{10}^{-2}}{5^{-6}\cdot 5^4}=\frac{{10}^{-2}}{5^{-2}}={\left(\frac{10}{5}\right)}^{-2}=2^{-2}={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$  

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g)

$\frac{6^4\cdot 9^{-4}}{4^2\cdot {12}^{-1}}=\frac{{\left(2\cdot 3\right)}^4\cdot 3^{-8}}{2^4\cdot {\left(3\cdot 4\right)}^{-1}}=\frac{2^4\cdot 3^4\cdot 3^{-8}}{2^4\cdot 3^{-1}\cdot 4^{-1}}=\frac{3^{-4}}{3^{-1}\cdot 4^{-1}}=\frac{3^{-3}}{4^{-1}}=$

$=\frac{{\left(\frac{1}{3}\right)}^3}{\frac{1}{4}}=\frac{1}{27}\cdot 4=\frac{4}{27}$   

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h)

$\frac{{16}^{-2}\cdot {125}^{-3}}{{10}^{-4}\cdot {25}^{-2}}=\frac{2^{-8}\cdot 5^{-9}}{{\left(2\cdot 5\right)}^{-4}\cdot 5^{-4}}=\frac{2^{-8}\cdot 5^{-9}}{2^{-4}\cdot 5^{-4}\cdot 5^{-4}}=\frac{2^{-8}\cdot 5^{-9}}{2^{-4}\cdot 5^{-8}}=$  

$=2^{-4}\cdot 5^{-1}={\left(\frac{1}{2}\right)}^4\cdot \frac{1}{5}=\frac{1}{16}\cdot \frac{1}{5}=\frac{1}{80}$