# How do you write 7^(1/2) * 3^(5/3 ) in radical form?

Feb 14, 2017

$= \sqrt{7} \times {\sqrt[3]{3}}^{5}$

#### Explanation:

Note the law of indices which states: ${x}^{\frac{p}{q}} = {\left(\sqrt[q]{x}\right)}^{p}$

${7}^{\frac{1}{2}} \cdot {3}^{\frac{5}{3}}$

The denominator of the index shows the root.
The numerator shows the power.

$= \sqrt{7} \times {\sqrt[3]{3}}^{5}$

Because different roots are being found, this cannot be combined into a single radical.