Answer
$y=\pm(a^{2/3}-x^{2/3})^{3/2}$
Work Step by Step
We solve this equation for $y$:
$x^{2/3}+y^{2/3}=a^{2/3}$
$y^{2/3}=a^{2/3}-x^{2/3}$
We cube both sides:
$(y^{2/3})^{3}=(a^{2/3}-x^{2/3})^{3}$
$y^{2*3/3}=a^{2*3/3}-x^{2*3/3}$
$y^{2}=(a^{2/3}-x^{2/3})^{3}$
We take the square root of both sides:
$y=\pm\sqrt{(a^{2/3}-x^{2/3})^{3}}$
$y=\pm(a^{2/3}-x^{2/3})^{3/2}$