Simplify and express the result as a product of prime powers and powers of variables.

MATHEMATICS · Single correct · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Simplify

\left(\dfrac{8x^{-2}y}{12x\,y^{-3}}\right)^{\frac{3}{2}}

and express the result as a product of prime powers and powers of variables. (a)

2^{-3/2}3^{3/2}x^{-9/2}y^{6}

(b)

2^{3/2}3^{-3/2}x^{9/2}y^{6}

(c)

2^{3/2}3^{-3/2}x^{-9/2}y^{6}

(d)

2^{3/2}3^{-3/2}x^{-9/2}y^{-3}