91Ó°ÊÓ

Here we have given radical expressions are:

$\sqrt{21p},\sqrt[4]{8q},4\sqrt[6]{36r}$

For any positive integer n and m, any radical in the form $\sqrt[n]{a^m}$can be written using fractional exponent in the form $a^{\frac{m}{n}}$.

If$\sqrt[n]{a}$is a real number and$nâ‰\yen 2$then$\sqrt[n]{a}=a^{\frac{1}{n}}$.

We have radical expression is,

$\sqrt{21p}$

Here we have square root so it can be written as the half power of 21p.

Therefore, $\sqrt{21p}$can be written as${\left(21p\right)}^{\frac{1}{2}}$.

Hence, rational exponent form of the given radical$\sqrt{21p}$is${\left(21p\right)}^{\frac{1}{2}}$.

We have given radical expression is,

$\sqrt[4]{8q}$.

Here we have radical expression is with 4^th root so we can write it in the $\frac{1}{4}$^th power of 8q.

Therefore$\sqrt[4]{8q}={\left(8q\right)}^{\frac{1}{4}}$

Hence, rational expression form of the radical$\sqrt[4]{8q}$is${\left(8q\right)}^{\frac{1}{4}}$.

Here we have given radical expression is,

$4\sqrt[6]{36r}$with 6^th root.

So we can rewrite it in to the $\frac{1}{6}$^th power of 36r.

Therefore,$4\sqrt[6]{36r}=4{\left(36r\right)}^{\frac{1}{6}}$.

Hence, fractional exponent of the radical$4\sqrt[6]{36r}$is$4{\left(36r\right)}^{\frac{1}{6}}$.