did I do this correctly?

[flew62999]

Simplify:

(2xy^3)^2
------------
(x^2y^-1)^3

my answer

4x^2y^6
----------
x^6y^-3

= 4y^3
-------
x^4

did I do this right?

 

[stapel]

You were good until the last step. Remember that, when you switch sides, the exponent switches signs. That's why, when you moved the x² from the numerator to the denominator, it became x^-2, so you had x^6-2 = x⁴. So when you moved the y^-3 to the other side, it became y³, so you should have ended up with y⁶⁺³ = y⁹.

Correct that bit, and you'll have the right answer.

Eliz.

P.S. Thank you for showing your steps!