$\text{a)}\left(3^{-4}\cdot 3^5\right):3^{-6}=3^{-4+5}:3^{-6}=3^1:3^{-6}=3^{1-\left(-6\right)}=3^{1+6}=3^7$  

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$\text{b)}\left({\left(-8\right)}^4\cdot {\left(-8\right)}^{-3}\right):{\left(-8\right)}^{-4}={\left(-8\right)}^{4-\left(-3\right)}:{\left(-8\right)}^{-4}={\left(-8\right)}^{4+3}:{\left(-8\right)}^{-4}=$  

$={\left(-8\right)}^7:{\left(-8\right)}^{-4}={\left(-8\right)}^{7-\left(-4\right)}={\left(-8\right)}^{7+4}={\left(-8\right)}^{11}$  

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$\text{c)}\left({\left(\frac{2}{3}\right)}^{-4}:{\left(\frac{2}{3}\right)}^{-3}\right)\cdot {\left(\frac{2}{3}\right)}^6={\left(\frac{2}{3}\right)}^{-4-\left(-3\right)}\cdot {\left(\frac{2}{3}\right)}^6={\left(\frac{2}{3}\right)}^{-4+3}\cdot {\left(\frac{2}{3}\right)}^6=$  

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

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$\text{d)}\left({\left(0,2\right)}^{-6}\cdot {\left(0,2\right)}^4\right):{\left(-0,2\right)}^{-4}={\left(0,2\right)}^{-6+4}:{\left(-0,2\right)}^{-4}={\left(0,2\right)}^{-2}:{\left(-0,2\right)}^{-4}=$  

$={\left(0,2\right)}^{-2-\left(-4\right)}={\left(0,2\right)}^{-2+4}={\left(0,2\right)}^2$  

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$\text{e)}\left({\left(\frac{1}{4}\right)}^{-7}:{\left(\frac{1}{4}\right)}^5\right)\cdot \left({\left(\frac{1}{4}\right)}^{-2}:{\left(\frac{1}{4}\right)}^{-4}\right)={\left(\frac{1}{4}\right)}^{-7-5}\cdot {\left(\frac{1}{4}\right)}^{-2-\left(-4\right)}=$  

$={\left(\frac{1}{4}\right)}^{-12}\cdot {\left(\frac{1}{4}\right)}^{-2+4}={\left(\frac{1}{4}\right)}^{-12}\cdot {\left(\frac{1}{4}\right)}^2={\left(\frac{1}{4}\right)}^{-12+2}={\left(\frac{1}{4}\right)}^{-10}$  

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$\text{f)}\left(5^5:5^{-3}\right):\left({\left(-5\right)}^{-6}:5^4\right)=5^{5-\left(-3\right)}:\left(5^{-6}:5^4\right)=5^{5+3}:5^{-6+4}=5^8:5^{-2}=5^{8-\left(-2\right)}=$  

$=5^{8+2}=5^{10}$  

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$\text{g)}\left({\left(2\frac{1}{2}\right)}^{-3}\cdot {\left(2\frac{1}{2}\right)}^4\right)\cdot \left({\left(-2\frac{1}{2}\right)}^{-7}:{\left(2\frac{1}{2}\right)}^{-8}\right)=$  

$={\left(2\frac{1}{2}\right)}^{-3+4}\cdot \left(-{\left(2\frac{1}{2}\right)}^{-7}:{\left(2\frac{1}{2}\right)}^{-8}\right)={\left(2\frac{1}{2}\right)}^1\cdot \left(-{\left(2\frac{1}{2}\right)}^{-7-\left(-8\right)}\right)=$  

$=2\frac{1}{2}\cdot \left(-{\left(2\frac{1}{2}\right)}^{-7+8}\right)=2\frac{1}{2}\cdot \left(-{\left(2\frac{1}{2}\right)}^1\right)=2\frac{1}{2}\cdot \left(-2\frac{1}{2}\right)=-{\left(2\frac{1}{2}\right)}^2$  

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$\text{h)}\left({\left(-0,2\right)}^4\cdot {0,2}^{-3}\right):{\left(-0,2\right)}^{-1}={\left(-0,2\right)}^{4-\left(-3\right)}:{\left(-0,2\right)}^{-1}=$  

$={\left(-0,2\right)}^{4+3}:{\left(-0,2\right)}^{-1}={\left(-0,2\right)}^7:{\left(-0,2\right)}^{-1}={\left(-0,2\right)}^{7-\left(-1\right)}=$  

$={\left(-0,2\right)}^{7+1}={\left(-0,2\right)}^8$