To simplify the given radical expression:

[ \frac{\sqrt[4]{x^9}}{\sqrtThe expression provided is:

[$4]{x^3\frac{11 \sqrt{9x}}{4 \}} sqrt{3}}$

\We]

are tasked with simplifying this radical expression.

Steps toWe can approach simplify it:

step1. Simplify individual square roots by:

• For $\sqrt{9x}$, we can separate the square root into step two parts: $$$$

sqrt{9x---

} = \sqrt{###9} \cdot Step \sqrt{x } = 3 \1sqrt{x:}$$ Apply - So the expression becomes the: \ [ \frac{11property \cd ofot 3 ex \sqrt{x}}{ponents4 \sqrt{3}} = under \frac{33 \sqrt{x the}} same{4 \sqrt{ radical3}} . ]

2.The Simplify the fraction property: is We can now simplify:

the square roots in the\ numerator and the[ denominator. To combine the square\ roots, we'll rationalize the denominator by multiplyingfrac both{\ the numerator and the denominator bysqrt \sqrt[n{3}:

]{ \frac{33a \sqrt}}{x}}{4 \{\sqrt{3sqrt}} \cdot \frac[n{\sqrt{3}}]{{\sqrtb{3}} = \frac{33 \sqrt{3x}}{4 \cd}}ot = 3}

Simplifying the denominator: [ \ = \frac{33 \sqrt{3sqrtx}}{12}