(4x to the -4th power times y to the 7th power) to the 2nd power over 24x to the power of -6 times y to the power of 2

Question

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

Answer 1

Im assuming it looks like this:

(4x^-4y⁷)² / 24x^-6y²

Here's my preferred method.

1) Distribute the square on the numerator

16x^-8y¹⁴

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

16/24 = 2/3

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

y¹⁴/y² = y^14-2 = y¹²

Now we have this.

(2x^-2y¹²)/3

Move negative powers down to the numerator.

(2y¹²)/3x²