How do you write the radical expression of $4 d^{\frac{3}{8}}$ $4d^(3/8)$ ?

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Answer 1 · 2015-06-27T21:11:20

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

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

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

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

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

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

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

How do you write the radical expression of 4d^(3/8)4d384d^(3/8)?