Question

Simply
(3x^2 y^3/x^3)^3

Answer 1

`=(27y^9)/(x^3)`

Explanation:

`\left((3x^2y^3)/(x^3)\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left((a)/(b)\right)^c=(a^c)/(b^c)\\\left((3x^2y^3)/(x^3)\right)^3=(\left(3x^2y^3\right)^3)/(\left(x^3\right)^3)\\=(\left(3x^2y^3\right)^3)/(\left(x^3\right)^3)\\\mathrm{Simplify}\:\left(3x^2y^3\right)^3:\quad 27x^6y^9\\=(27x^6y^9)/(\left(x^3\right)^3)\\\mathrm{Simplify}\:\left(x^3\right)^3:\quad x^9\\=(27x^6y^9)/(x^9)\\\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)=(1)/(x^(b-a))`

`(x^6)/(x^9)=(1)/(x^(9-6))\\(x^6)/(x^9)=(1)/(x^(9-6))\\=(27y^9)/(x^(9-6))\\\mathrm{Subtract\:the\:numbers:}\:9-6=3\\=(27y^9)/(x^3)`