Question

Simplify each of the following
$\begin{array}{cc}& i)(\sqrt{5}{)}^{-3}(\sqrt{2}{)}^{-3}\\ & ii)\frac{1}{\sqrt[3]{34^{-5}}}\\ & iii)(25{)}^{-1/3}\times \sqrt[3]{316}\\ & iv)(\sqrt[3]{38}{)}^{-1/2}\end{array}$

Answer 1

$\left(i\right){\left(\sqrt{5}\right)}^{-3}\times {\left(\sqrt{2}\right)}^{-3}={\left(10\right)}^{-\frac{3}{2}}={\left(\sqrt{10}\right)}^{-3}\left(ii\right)\frac{1}{\sqrt[3]{34^{-5}}}=4^{\frac{5}{3}}=\sqrt[3]{34^5}\left(iii\right){\left(25\right)}^{-\frac{1}{3}}\times \sqrt[3]{316}=\sqrt[3]{3\frac{16}{25}}={(2^4\times 5^{-2})}^{\frac{1}{3}}\left(iv\right){\left(\sqrt[3]{38}\right)}^{-\frac{1}{2}}={\left(2\right)}^{-\frac{1}{2}}=\frac{1}{\sqrt{2}}$