$a)$     ${\left(\frac{1}{125}\right)}^{-\frac{1}{3}}={\left(125\right)}^{\frac{1}{3}}=\sqrt[3]{125}=\sqrt[3]{5^3}={\left(\sqrt[3]{5}\right)}^3=5$  

${\left(\frac{9}{16}\right)}^{-\frac{1}{2}}={\left(\frac{16}{9}\right)}^{\frac{1}{2}}=\sqrt{\frac{16}{9}}=\frac{\sqrt{16}}{\sqrt{9}}=\frac{4}{3}=1\frac{1}{3}$  

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

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$b)$      ${64}^{\frac{1}{6}}=\sqrt[6]{64}=\sqrt[6]{2^6}={\left(\sqrt[6]{2}\right)}^6=2$  

${\left(\frac{25}{49}\right)}^{-0,5}={\left(\frac{25}{49}\right)}^{-\frac{1}{2}}={\left(\frac{49}{25}\right)}^{\frac{1}{2}}=\sqrt{\frac{49}{25}}=\frac{\sqrt{49}}{\sqrt{25}}=\frac{7}{5}=1\frac{2}{5}$  

${0,25}^{-\frac{1}{2}}={\left(\frac{1}{4}\right)}^{-\frac{1}{2}}=4^{\frac{1}{2}}=\sqrt{4}=2$  

${\left(\frac{25}{36}\right)}^{-\frac{1}{2}}={\left(\frac{36}{25}\right)}^{\frac{1}{2}}=\sqrt{\frac{36}{25}}=\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}=1\frac{1}{5}$

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$c)$     ${\left(2\frac{1}{4}\right)}^{-\frac{3}{2}}={\left(\frac{9}{4}\right)}^{-\frac{3}{2}}={\left(\frac{4}{9}\right)}^{\frac{3}{2}}=\sqrt{{\left(\frac{4}{9}\right)}^3}={\left(\sqrt{\frac{4}{9}}\right)}^3={\left(\frac{\sqrt{4}}{\sqrt{9}}\right)}^3={\left(\frac{2}{3}\right)}^3=$  

$=\frac{2^3}{3^3}=\frac{8}{27}$  

${\left(2\frac{93}{125}\right)}^{-\frac{1}{3}}={\left(\frac{343}{125}\right)}^{-\frac{1}{3}}={\left(\frac{125}{343}\right)}^{\frac{1}{3}}=\sqrt[3]{\frac{125}{343}}=\frac{\sqrt[3]{125}}{\sqrt[3]{343}}=\frac{\sqrt[3]{5^3}}{{\sqrt[3]{7}}^3}=\frac{5}{7}$  

${\left(7\frac{9}{16}\right)}^{\frac{1}{2}}={\left(\frac{121}{16}\right)}^{\frac{1}{2}}=\sqrt{\frac{121}{16}}=\frac{\sqrt{121}}{\sqrt{16}}=\frac{11}{4}=2\frac{3}{4}$

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$d)$     ${\left(\frac{125}{64}\right)}^{-\frac{2}{3}}={\left(\frac{64}{125}\right)}^{\frac{2}{3}}=\sqrt[3]{{\left(\frac{64}{125}\right)}^2}={\left(\sqrt[3]{\frac{64}{125}}\right)}^2={\left(\frac{\sqrt[3]{64}}{\sqrt[3]{125}}\right)}^2={\left(\frac{\sqrt[3]{4^3}}{\sqrt[3]{5^3}}\right)}^2=$  

$={\left(\frac{4}{5}\right)}^2=\frac{4^2}{5^2}=\frac{16}{25}$  

${\left(\frac{27}{8}\right)}^{\frac{2}{3}}=\sqrt[3]{{\left(\frac{27}{8}\right)}^2}={\left(\sqrt[3]{\frac{27}{8}}\right)}^2={\left(\frac{\sqrt[3]{27}}{\sqrt[3]{8}}\right)}^2={\left(\frac{\sqrt[3]{3^3}}{\sqrt[3]{2^3}}\right)}^2={\left(\frac{3}{2}\right)}^2=\frac{3^2}{2^2}=$  

$=\frac{9}{4}=2\frac{1}{4}$  

${\left(\frac{625}{81}\right)}^{-\frac{1}{2}}={\left(\frac{81}{625}\right)}^{\frac{1}{2}}=\sqrt{\frac{81}{625}}=\frac{\sqrt{81}}{\sqrt{625}}=\frac{9}{25}$  

${\left(6\frac{1}{4}\right)}^{-1\frac{1}{2}}={\left(\frac{25}{4}\right)}^{-\frac{3}{2}}={\left(\frac{4}{25}\right)}^{\frac{3}{2}}=\sqrt{{\left(\frac{4}{25}\right)}^3}={\left(\sqrt{\frac{4}{25}}\right)}^3={\left(\frac{\sqrt{4}}{\sqrt{25}}\right)}^3=$  

$={\left(\frac{2}{5}\right)}^3=\frac{2^3}{5^3}=\frac{8}{125}$  

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$e)$     ${0,49}^{-\frac{1}{2}}={\left(\frac{49}{100}\right)}^{-\frac{1}{2}}={\left(\frac{100}{49}\right)}^{\frac{1}{2}}=\sqrt{\frac{100}{49}}=\frac{\sqrt{100}}{\sqrt{49}}=\frac{10}{7}=1\frac{3}{7}$  

${0,125}^{\frac{2}{3}}={\left(\frac{1}{8}\right)}^{\frac{2}{3}}=\sqrt[3]{{\left(\frac{1}{8}\right)}^2}={\left(\sqrt[3]{\frac{1}{8}}\right)}^2={\left(\frac{\sqrt[3]{1}}{\sqrt[3]{8}}\right)}^2={\left(\frac{\sqrt[3]{1^3}}{\sqrt[3]{2^3}}\right)}^2={\left(\frac{1}{2}\right)}^2=$  

$=\frac{1^2}{2^2}=\frac{1}{4}=0,25$  

${0,027}^{-\frac{2}{3}}={\left(\frac{27}{1000}\right)}^{-\frac{2}{3}}={\left(\frac{1000}{27}\right)}^{\frac{2}{3}}=\sqrt[3]{{\left(\frac{1000}{27}\right)}^2}={\left(\sqrt[3]{\frac{1000}{27}}\right)}^2=$

  $={\left(\frac{\sqrt[3]{1000}}{\sqrt[3]{27}}\right)}^2={\left(\frac{\sqrt[3]{{10}^3}}{\sqrt[3]{3^3}}\right)}^2={\left(\frac{10}{3}\right)}^2=\frac{{10}^2}{3^2}=\frac{100}{9}=11\frac{1}{9}$  

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$f)$     ${0,04}^{\frac{3}{2}}={\left(\frac{4}{100}\right)}^{\frac{3}{2}}=\sqrt{{\left(\frac{4}{100}\right)}^3}={\left(\sqrt{\frac{4}{100}}\right)}^3={\left(\frac{\sqrt{4}}{\sqrt{100}}\right)}^3={\left(\frac{2}{10}\right)}^3=\frac{2^3}{{10}^3}=$  

$=\frac{8}{1000}=0,008$  

${0,0001}^{-1\frac{1}{4}}={\left(\frac{1}{10000}\right)}^{-\frac{5}{4}}={\left(10000\right)}^{\frac{5}{4}}=\sqrt[4]{{10000}^5}={\left(\sqrt[4]{10000}\right)}^5={\left(\sqrt[4]{{10}^4}\right)}^5=$

$={10}^5=100000$   

${0,125}^{-\frac{1}{3}}={\left(\frac{125}{1000}\right)}^{-\frac{1}{3}}={\left(\frac{1}{8}\right)}^{-\frac{1}{3}}=8^{\frac{1}{3}}=\sqrt[3]{8}=\sqrt[3]{2^3}=2$