Compute:
$xvi.(27{)}^{\frac{2}{3}}÷{\left(\frac{81}{16}\right)}^{\frac{-1}{4}}$

Evaluate : ${27}^{\frac{2}{3}}+(\frac{81}{16}{)}^{\frac{-1}{4}}$

Prove that :

$\left(i\right)(\sqrt{3\times 5^{-3}}÷\sqrt[3]{33^{-1}}\sqrt{5})\times \sqrt[6]{63\times 5^6}=\frac{3}{5}\left(ii\right)9^{\frac{3}{2}}-3\times 5^0-{\left(\frac{1}{81}\right)}^{\frac{-1}{2}}=15\left(iii\right){\left(\frac{1}{4}\right)}^{-2}-3\times 8^{\frac{2}{3}}\times 4^0+{\left(\frac{9}{16}\right)}^{\frac{-1}{2}}=\frac{16}{3}\left(iv\right)\frac{2^{\frac{1}{2}}\times 3^{\frac{1}{3}}\times 4^{\frac{1}{4}}}{{10}^{\frac{-1}{5}}\times 5^{\frac{3}{5}}}÷\frac{3^{\frac{4}{3}}\times 5^{\frac{-7}{5}}}{4^{\frac{-3}{5}}\times 6}=10\left(v\right)\sqrt{\frac{1}{4}}+(0.01{)}^{\frac{-1}{2}}-(27{)}^{\frac{2}{3}}=\frac{3}{2}\left(vi\right)\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{3}{2}\left(vii\right){\left(\frac{64}{125}\right)}^{\frac{-2}{3}}+\frac{1}{{\left(\frac{256}{625}\right)}^{\frac{1}{4}}}+{\left(\frac{\sqrt{25}}{\sqrt[3]{364}}\right)}^0=\frac{61}{16}\left(viii\right)\frac{3^{-3}\times 6^2\times \sqrt{98}}{5^2\times \sqrt[3]{3\frac{1}{25}}\times (15{)}^{\frac{-4}{3}}\times 3^{\frac{1}{3}}}=28\sqrt{2}\left(ix\right)\frac{(0.6{)}^0-(0.1{)}^{-1}}{{\left(\frac{3}{8}\right)}^{-1}{\left(\frac{3}{2}\right)}^3+{\left(\frac{1}{3}\right)}^{-1}}=-\frac{3}{2}$