Exponent Laws Question?

Question

(x^6 y^-5) (x^-2 y^-2)^3
__________________
(xy^2)^-1

NOTE: thats all one question

I keep getting x^-1 /y^-9 but apparently the answer is x/y^9. Can anyone verify if x/y^9 is the correct answer?

Answer 1

First the part (x^-2 y^-2)^3 = (x^-6 y^-6) So the x^6 and x^-6 cancel on top leaving x^0 = 1 on top the y parameter becomes y^-11

The bottom becomes x^-1 y^-2 when the bottom terms are moved to the top the exponents become the negative of what they were so you get x^1 y^2 combining with the y^-11 on the top I get x^1 y^-9 or x y^-9 if the y^-9 is moved to the bottom then x / y^9 is the answer

Answer 2

(x^6 y^-5) (x^-2 y^-2)^3
__________________
(xy^2)^-1


(x^6 Y^-5) (x^-6 y^-6)
---------------------------
(xy^2)^-1


x^0 y^-11
-----------
(xy^2)^-1


xy^2
--------
y^11


x
---
y^9

Answer 3

I got x/y^9........