Question

Rewrite the following radical expression in rational exponent form. (√x)5

Answer 1

If you meant:
$( \sqrt{x})^5$

Then, let's change the square to read:
$(x^ \frac{1}{2})^5$

Now, we can just multiply the two powers, and your answer is:
$x^ \frac{5}{2}$

Hope I helped.

Answer 2

Answer:

The rational exponent form of given expression is $x^{\frac{5}{2}}$.

Step-by-step explanation:

A number is called a rational number if it can be defined as p/q, where p and q are real numbers and q≠0.

The given expression is

$(\sqrt{x})^5$

It can be written as

$(\sqrt{x})^5=(x^{\frac{1}{2}})^5$              $[\because \sqrt{x}=(x)^{\frac{1}{2}}]$

Using the power property of exponent we get

$(\sqrt{x})^5=x^{\frac{5}{2}}$              $[\because (x^m)^n=x^{mn}]$

Here $\frac{5}{2}$ is a rational number.

Therefore the rational exponent form of given expression is $x^{\frac{5}{2}}$.