Obliczmy wartość podanych wyrażeń:

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

$=\frac{{\left(-2\right)}^{10}}{{\left(-2\right)}^9}={\left(-2\right)}^{10-9}={\left(-2\right)}^1=-2$  

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$b\text{)}{\left[{\left(3\frac{1}{3}\right)}^{-1}-5^{-1}\right]}^{-1}={\left[{\left(\frac{10}{3}\right)}^{-1}-5^{-1}\right]}^{-1}={\left[\frac{3}{10}-\frac{1}{5}\right]}^{-1}=$   

$={\left[\frac{3}{10}-\frac{2}{10}\right]}^{-1}={\left[\frac{1}{10}\right]}^{-1}=10$  

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$c\text{)}\frac{\sqrt[3]{25}\cdot 5^{\frac{1}{3}}}{5^{\frac{4}{3}}\cdot 5^{\frac{2}{3}}}=\frac{{25}^{\frac{1}{3}}\cdot 5^{\frac{1}{3}}}{5^{\frac{4}{3}+\frac{2}{3}}}=\frac{{\left(5^2\right)}^{\frac{1}{3}}\cdot 5^{\frac{1}{3}}}{5^{\frac{6}{3}}}=\frac{5^{\frac{2}{3}}\cdot 5^{\frac{1}{3}}}{5^2}=$  

$=\frac{5^{\frac{2}{3}+\frac{1}{3}}}{5^2}=\frac{5^{\frac{3}{3}}}{5^2}=\frac{5}{5^2}=5^{1-2}=5^{-1}=\frac{1}{5}$  

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$d\text{)}{\left[{\left({64}^2\right)}^0\right]}^{\frac{1}{2}}=\sqrt{{\left({64}^2\right)}^0}=\sqrt{1}=1$