# What is the radical expression of 4d ^(3/8)?

Nov 17, 2016

$4 {d}^{\frac{3}{8}} = 4 \cdot \sqrt[8]{{d}^{3}} = 4 \cdot {\left(\sqrt[8]{d}\right)}^{3}$

#### Explanation:

Recall a law of indices which deals with fractional indices.

${x}^{\frac{p}{q}} = {\sqrt[q]{x}}^{p}$

The numerator of the index indicates the power and the denominator indicates the root.

$4 {d}^{\frac{3}{8}} = 4 \cdot \sqrt[8]{{d}^{3}} = 4 \cdot {\left(\sqrt[8]{d}\right)}^{3}$

Note 2 things:

• The index only applies to the base 'd', not to the 4 as well
• The power 3 can be under the root or outside the root