# How do you write the radical expression of 4d^(3/8)?

Jun 27, 2015

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

#### Explanation:

The exponent $\frac{3}{8}$ applies only to the $d$. (Not to the $4$ we are multiplying by.)

An rational exponent $\frac{m}{n}$ means take the $n$ root, of the $m$ power (Or the $m$ power of the $n$ root.)

So we need the $8$ root of the $3$ power: $4 \sqrt[8]{{d}^{3}}$

(Or the $3$ power of the $8$ root: $4 {\left(\sqrt[8]{d}\right)}^{3}$

As long as $\frac{m}{n}$ is already reduced to lowest terms, the two expressions are equal:

$\sqrt[n]{{x}^{m}} = {\left(\sqrt[n]{x}\right)}^{m}$