Question

How do you simplify `((3x^-1) / (6y^-3)) ^-2`?

Answer 1

I got `(4x^2)/y^6` pretty sure it's right I checked

Explanation:

There are plenty of ways to start, I like dealing with the inside first.

So to start you have to flip the `x^-1` and the `y^-3` but make sure not to bring the whole numbers with the variables because the exponents are only attached to the `x` and `y`.
After you flip the variables you should get `((3y^3)/(6x))^-2` .
Once you do that you can reduce the 3 and 6 to make `((y^3)/(2x))^-2`. After that you have to flip the entire thing to make the outside `-2` positive: `((2x)/(y^3))^2`. After that just distribute the 2 and it becomes `(4x^2)/(y^6)`.
Remember if you combine terms without the parenthesis the exponents just add but with parenthesis the exponent must multiply to everything which is why the 2 became 4.