# How do you write 2^(7 / 8)/2^(1/4)  as a radical?

Jun 5, 2016

$\sqrt[8]{32}$

#### Explanation:

first do division
${2}^{\frac{7}{8} - \frac{1}{4}}$
${2}^{\frac{5}{8}}$
then it is equivalent to the radical
${\sqrt[8]{2}}^{5}$
or
$\sqrt[8]{32}$

Jun 5, 2016

${2}^{\frac{5}{8}} = {\sqrt[8]{2}}^{5}$

#### Explanation:

Using the law of indices for dividing if the bases are the same, we can simplify the f,raction by subtracting the indices to get

${2}^{\frac{5}{8}}$

The law of indices involving fractional indices states

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

So, ${2}^{\frac{5}{8}} = {\sqrt[8]{2}}^{5}$

The denominator becomes the root and the numerator becomes the power - it can be inside or outside the root sign.