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

1 Answer
Apr 11, 2018

Answer:

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.