# Evaluate the following ?

Oct 27, 2016

${256}^{\frac{5}{2}} = {\sqrt{256}}^{5}$

=${16}^{5} = 1 , 048 , 576$

#### Explanation:

${256}^{4 - \frac{3}{2}}$

Evaluate means find the value of the expression - you need a number answer.

In the exponent there is $4 - \frac{3}{2}$
This is the same as $4 - 1 \frac{1}{2}$ which is $2 \frac{1}{2}$

$2 \frac{1}{2} = \frac{5}{2}$

So we have: ${256}^{\frac{5}{2}}$

Recall the law: ${x}^{\frac{p}{q}} = {\left(\sqrt[q]{x}\right)}^{p}$

The denominator in the index shows a root and the numerator shows a power.

${256}^{\frac{5}{2}} = {\sqrt{256}}^{5}$

=${16}^{5}$

=$1 , 048 , 576$