# Question #d5343

Jul 4, 2017

$x = 4$

#### Explanation:

I will assume that you want to solve the following equality for $x$:

${x}^{\frac{5}{2}} = 32$

Using our index laws we can rewrite the left hand side as:

${x}^{\frac{5}{2}} = {\left({x}^{\frac{1}{2}}\right)}^{5}$

and the right hand side as:

$32 = {2}^{5}$

Now we can write both sides of the equality with the same exponent:

${\left({x}^{\frac{1}{2}}\right)}^{5} = {\left(2\right)}^{5}$

The terms in the brackets must be equal to each other, so:

${x}^{\frac{1}{2}} = 2$

Square both sides:

${\left({x}^{\frac{1}{2}}\right)}^{2} = {2}^{2}$

$\Rightarrow x = 4$