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

Apr 11, 2018

I got $\frac{4 {x}^{2}}{y} ^ 6$ 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 ${\left(\frac{3 {y}^{3}}{6 x}\right)}^{-} 2$ .
Once you do that you can reduce the 3 and 6 to make ${\left(\frac{{y}^{3}}{2 x}\right)}^{-} 2$. After that you have to flip the entire thing to make the outside $- 2$ positive: ${\left(\frac{2 x}{{y}^{3}}\right)}^{2}$. After that just distribute the 2 and it becomes $\frac{4 {x}^{2}}{{y}^{6}}$.
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.