Question

4(3xy^4)^3/(2x^3y^5)^4

Answer 1

`(4\left(3xy^4\right)^3)/(\left(2x^3y^5\right)^4)=(27)/(4x^9y^8)`

Explanation:

Given the expression

`\:\:(4\left(3xy^4\right)^3)/(\left(2x^3y^5\right)^4)`

solving the expression

`\:\:(4\left(3xy^4\right)^3)/(\left(2x^3y^5\right)^4)=4\cdot \:(\left(3xy^4\right)^3)/(\left(2x^3y^5\right)^4)`

`=4\:(27x^3y^(12))/(16x^(12)y^(20))`

`=4\cdot (3^3)/(2^4x^9y^8)`

The multiply fractions are defined as

`\:a\cdot (b)/(c)=(a\:\cdot \:b)/(c)`

so the expression becomes

`=(3^3\cdot \:4)/(2^4x^9y^8)`

`=(3^3\cdot \:2^2)/(2^4x^9y^8)`

`=(3^3)/(2^2x^9y^8)`

Refining

`=(27)/(4x^9y^8)`

Therefore,

`(4\left(3xy^4\right)^3)/(\left(2x^3y^5\right)^4)=(27)/(4x^9y^8)`