Answer
$\dfrac{x^{3}}{y^{6}}$
Work Step by Step
When a fraction is raised to a power, the exponent applies to both the numerator as well as the denominator. Because both numerator and denominator already have exponents, we will need to multiply the exponents inside the parentheses with the one outside them. Let's rewrite the problem to reflect this:
$=\dfrac{\left(x^{1/3}\right)^{9}}{\left(y^{2/3}\right)^{9}}\\
\\=\dfrac{x^{(1/3)(9)}}{y^{(2/3)(9)}}\\
\\=\dfrac{x^3}{y^6}\\
$
