$\text{a)}$  

$216=6^3$  

$576=64\cdot 9=2^6\cdot 3^2$  

$243=3^5$  

$392=8\cdot 49=2^3\cdot 7^2$  

$125=5^3$  

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$\text{b)}$  

$2\frac{7}{9}=\frac{25}{9}={\left(\frac{5}{3}\right)}^2$  

$-3\frac{3}{8}=-\frac{27}{8}={\left(-\frac{3}{2}\right)}^3$  

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

$-2\frac{27}{10}=-\frac{64}{27}={\left(-\frac{4}{3}\right)}^3$  

$5\frac{1}{16}=\frac{81}{16}={\left(\frac{3}{2}\right)}^4$