Answer
$\displaystyle \frac{2x^{3}}{y}$
Work Step by Step
$(8x^{-6}y^{3})^{1/3}(x^{5/6}y^{-1/3})^{6}=\qquad$... apply $(ab)^{n}=a^{n}b^{n}$
.... recognize $8=2^{3}$
$=(2^{3})^{1/3}x^{-6(1/3)}y^{3(1/3)}x^{(5/6)(6)}y^{(-1/3)(6)}$
$=2x^{-2}y^{1}x^{5}y^{-2}\qquad$... apply $a^{m}a^{n}=a^{m+n}$
$=2x^{-2+5}y^{1+(-2)}$
$=2x^{3}y^{-1}\qquad$... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$
$=\displaystyle \frac{2x^{3}}{y}$
