$\text{a)}\left(2^4\cdot 2^5\right):2^8=2^{4+5}:2^8=2^9:2^8=2^{9-8}=2^1=2$  

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$\text{b)}\left(7^2\cdot 7\right)\cdot 7=7^{2+1}\cdot 7=7^3\cdot 7=7^{3+1}=7^4=2401$   

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$\text{c)}\left({\left(\frac{1}{3}\right)}^5:{\left(\frac{1}{3}\right)}^2\right):{\left(\frac{1}{3}\right)}^2={\left(\frac{1}{3}\right)}^{5-2}:{\left(\frac{1}{3}\right)}^2={\left(\frac{1}{3}\right)}^3:{\left(\frac{1}{3}\right)}^2={\left(\frac{1}{3}\right)}^{3-2}=$  

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

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$\text{d)}\left({\left(-8\right)}^6\cdot {\left(-8\right)}^2\right):{\left(-8\right)}^4={\left(-8\right)}^{6+2}:{\left(-8\right)}^4={\left(-8\right)}^8:{\left(-8\right)}^4={\left(-8\right)}^{8-4}=$  

$={\left(-8\right)}^4=8^4=4096$  

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$\text{e)}\left({\left(\frac{1}{5}\right)}^7:{\left(\frac{1}{5}\right)}^3\right)\cdot (\left(\frac{1}{5^4}:{\left(\frac{1}{5}\right)}^2\right)={\left(\frac{1}{5}\right)}^{7-3}\cdot {\left(\frac{1}{5}\right)}^{4-2}={\left(\frac{1}{5}\right)}^4\cdot {\left(\frac{1}{5}\right)}^2=$  

$={\left(\frac{1}{5}\right)}^{4+2}={\left(\frac{1}{5}\right)}^6=\frac{1}{15625}$  

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$\text{f)}\left(4^5:4^2\right):\left({\left(-4\right)}^6:{\left(-4\right)}^5\right)=4^{5-2}:{\left(-4\right)}^{6-5}=4^3:{\left(-4\right)}^1=4^3:\left(-4\right)=$  

$=-4^3:4=-4^{3-1}=-4^2=-16$  

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$\text{g)}\left({\left(-2\right)}^3\cdot {\left(-2\right)}^4\right)\cdot 2^7:2^5)={\left(-2\right)}^{3+4}\cdot 2^{7-5}={\left(-2\right)}^7\cdot 2^2=-2^7\cdot 2^2=$  

$=-2^{7+2}=-2^9=-512$  

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$\text{h)}\left({\left(-0,1\right)}^4\cdot {0,1}^5\right):{\left(-0,1\right)}^8=\left({0,1}^4\cdot {0,1}^5\right):{0,1}^8={0,1}^{4+5}:{0,1}^8={0,1}^9:{0,1}^8=$  

$={0,1}^{9-8}=0,1$