Translating the words to mathematical representation we get

$\frac{x^2}{\sqrt[3]{x}} = 9x$

$x^2 = 9x \sqrt[3]{x}$

$x^2 = 9x \times x^{\frac{1}{3}}$

$x^2 = 9 \times x^{\frac{4}{3}}$

$x^2 = 9({x^\frac{2}{3}}^2)$

$x^2 = 3^2 \times ({x^\frac{2}{3}}^2)$

Taking the square root on both sides, we get

$x = 3 \times x^{\frac{2}{3}}$

rearranging the terms

$x \times x^{\frac{-2}{3}} = 3$

$x^{\frac{1}{3}} = 3$

cubing both sides to get the value of $x$ on the LHS

$x = 3^3$

$x=27$

The answer is D