Answer
$3x^{\frac{1}{2}}$
Work Step by Step
Applying the rules of exponents gives:
$\sqrt[4] 81x^2$
$=\sqrt[4] (9x)^2$
$=(9x)^{\frac{1}{2}}$
$=(3^2)^{\frac{1}{2}}x^{\frac{1}{2}}$
$=3x^{\frac{1}{2}}$
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