Question

Rewrite the following radical expression in rational exponent form

Answer 1

The roots can be written as exponents:
$\sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } \\ \\ { \sqrt[x]{a} }^{y} = {a}^{ \frac{y}{x} }$
In this problem, we know that the root is a square root because there is no number on the left side of the root.

So we could write that as:
${x}^{ \frac{5}{2} }$

Answer 2

$(\sqrt{x})^{5}$

Rewrite √ as the power of 1/2

⇒ $(x^{\frac{1}{2}})^{5}$

⇒$x^{\frac{5}{2}}$

$\text {Answer: } x^{\frac{5}{2}}$