# Thread: Trouble simplifing an exponental expression

1. ## Trouble simplifing an exponental expression

Here's the expression that I'm having trouble with (sorry for the lack of ease of readability):

((2^-1)(x^-2)(y^-1))^-2((2x^-4)(y^3))^-2((16x^-3)(y^3))^0 / ((2x^-3)(y^-5))^2

x^18y^6 / 4

I've worked this problem over and over as many different ways as I could, but I've never got the correct answer. I would appreciate very much it if someone could post the steps to solving this problem.

Thanks for your time!

2. Hello, ashepherd89!

Simplify: .$\displaystyle \frac{(2^{-1}x^{-2}y^{-1})^{-2}(2x^{-4}y^3)^{-2}(16x^{-3}y^3)^0} {(2x^{-3}y^{-5})^2}$

The answer is: .$\displaystyle \frac{x^{18}y^6}{4}$

We have: .$\displaystyle \frac{(2^{-1})^{-2}(x^{-2})^{-2}(y^{-1})^{-2}\cdot(2)^{-2}(x^{-4})^{-2}(y^3)^{-2}\cdot1} {2^2(x^{-3})^2(y^{-5})^2}$

. . $\displaystyle = \;\frac{2^2x^4y^2\cdot2^{-2}x^8y^{-6}}{4x^{-6}y^{-10}} \;=\;\frac{x^{12}y^{-4}}{4x^{-6}y^{-10}} \;=\;\frac{x^{18}y^6}{4}$

3. Great! Thank you very much Soroban!