What is the easiest way to do this?when you change it to the reciprocal, do the positives become negatives?

Im assuming it looks like this:

(4x^{-4}y^{7})^{2} / 24x^{-6}y^{2}

Here's my preferred method.

1) Distribute the square on the numerator

16x^{-8}y^{14}

2) Subtract bottom exponents from top exponents, of similar base.

16/24 = 2/3

x^{-8}/x^{-6} = x^{-8-(-6)}=x^{-2}

y^{14}/y^{2} = y^{14-2} = y^{12}

Now we have this.

(2x^{-2}y^{12})/3

Move negative powers down to the numerator.

(2y^{12})/3x^{2}