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

$\left(a\right)\sqrt[6]{{x}^{5}}$
To simplify:
The expression $\sqrt[6]{{x}^{5}}$ and express the answer using rational exponents.
(b) ${\left(\sqrt{x}\right)}^{9}$
To simplify:
The expression ${\left(\sqrt{x}\right)}^{9}$ and express the answer using rational exponents.

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Velsenw

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