Question

How do you divide `(x^2/y^3)^4`?

Answer 1

No division is necessary. They are not the same terms.

Split the exponent `[((x^l)/(y^n))^m = (x^l)^m/(y^n)^m]`:
`= (x^2)^4/(y^3)^4`

Apply the exponent `[(x^n)^m= x^(nm)]`:
`= (x^(2*4))/(y^(3*4))`

Finish:
`= color(blue)((x^8)/(y^12))`

Normally we do not write negative exponents in our answers by convention, so that is our final answer.