Radicals reduction to common index

We will try to reduce several radicals to common index , and we can do this by converting the fraction exponents of their expression as a power into a common denominator.

Example

$\sqrt{5} \cdot \sqrt[3]{2} = 5^{\frac{1}{2}} \cdot 2^{\frac{1}{3}} = 5^{\frac{3}{6}} \cdot 2^{\frac{2}{6}} = \sqrt[6]{5^{3}} \cdot \sqrt[6]{2^{2}} = \sqrt[6]{5^{3} \cdot 2^{2}} = \sqrt[6]{500}$