Question

HELP PLEASE!
simplify

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

Answer 1

`\large\boxed{((2x^3y)^3)/((4xy^2)^2(xy^3))=(x^6)/(2y^4)}`

Explanation:

`((2x^3y)^3)/((4xy^2)^2(xy^3))\qquad\text{use}\ (ab)^n\ \text{and}\ (a^n)^m=a^(nm)\\\\=(2^3(x^3)^3y^3)/(4^2x^2(y^2)^2xy^3)\qquad\text{cancel}\ y^3\\\\=(8x^((3)(3))y^3\!\!\!\!\!\diagup)/(16x^2y^((2)(2))xy^3\!\!\!\!\!\diagup)\\\\=(8\!\!\!\!\diagup^1x^9)/(16\!\!\!\!\!\diagup_2x^2y^4x)\qquad\text{use}\ a^na^m=a^(n+m)\\\\=(x^9)/(2x^(2+1)y^4)\\\\=(x^9)/(2x^3y^4)\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\=(x^(9-3))/(2y^4)\\\\=(x^6)/(2y^4)`