Question

How do you multiply and simplify `(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} ( \frac { y ^ { 2} } { 4x } ) ^ { 2}`?

Answer 1

`x^4/(2y^5)`

Explanation:

`(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} ( \frac { y ^ { 2} } { 4x } ) ^ { 2}`

Let's manage each fraction individually for now.

`(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} =(8x^6)/y^9`

`( \frac { y ^ { 2} } { 4x } ) ^ { 2}=y^4/(16x^2)`

Now we multiply. Remember that `x^a/x^b=x^(a-b)`.

`(8x^6)/y^9\cdoty^4/(16x^2)=x^4/(2y^5)`