Express the radical as power. (a) root(6)(x^5) (b) sqrt(x)^9

(a) Concept used:
If ais a real number, n is a positive integer and $\sqrt[n]{a^m}\text{is a real number then the rational exponent expression}{\displaystyle \sqrt[n]{a^m}\text{is equivalent to radical expression}{\displaystyle a^{\frac{m}{n}}.}}$
The above statement can be expressed as,
${\displaystyle {\sqrt[n]{a}}^m=a^{\frac{m}{n}}}$ ...... (1)
Calculation:
The given expression is ${\displaystyle \sqrt[6]{x^5}}$
Subtitute 6 for n, 5 for m and x for a in the equation (1) to obtain the equialent expression in rational exponent as,
${\displaystyle \sqrt[6]{x^5}={\left(x^{\frac{1}{6}}\right)}^5}$
${\displaystyle =x^{\frac{5}{6}}}$
Conclusion:
Thus, the equvalent expression of the expression ${\displaystyle \sqrt[6]{x^5}is{x}^{\frac{5}{6}}.}$
(b) Calculation:
The given expression is ${\displaystyle {\left(\sqrt{x}\right)}^9}$
Subtitute 2 for n, 9 for m and x for a in the equation (1) to obtain the equialent expression in rational exponent as,
${\displaystyle {\left(\sqrt{x}\right)}^9={\left(x^{\frac{1}{2}}\right)}^9}$
${\displaystyle =x^{\frac{9}{2}}}$
Conclusion:
Thus, the equivalent expression of the expression ${\displaystyle {\left(\sqrt{x}\right)}^{9}is{x}^{\frac{9}{2}}.}$