Simplify the following expression so that the final answer is written as a product of…

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

Simplify the following expression so that the final answer is written as a product of powers of the primes

2

and

3

and of the variables

x

and

y

, each with positive integer exponents only:

\frac{(18x^{3}y^{-2})^{\tfrac{3}{4}}\,(12x^{-5}y^{4})^{\tfrac{1}{2}}}{(3x^{-2}y)^{-\tfrac{3}{2}}}\times\left(\frac{27x^{6}}{8y^{3}}\right)^{\tfrac{1}{4}}.