Question

Please help! how do I simplify this

(2a^2b^-1)(-a^-3b^2)

Answer 1

\[(2a^{2}b^{-1})(-a^{-3}b^{2})\]
Get rid of the negative powers first:

\[(\frac{2a^{2}}{b})(\frac{-b^{2}}{a^{3}})\]
Now simplify from there.

Answer 2

will i have to expand it out and then simplify from what i have. Also, if its a negative do I always get rid of the negative powers first before doing any other step?

Answer 3

It is suggested to get rid of the negative powers, just to simplify the problem!
It ain't mandatory though! :)

Answer 4

I know, but do i have to do that first or does it matter when i get rid of them?

Answer 5

You're not really getting rid of them, just writing the formula in a way that's easier to visualize what's going on. For this particular problem you could just reorganize the a's and b's and add the powers:

\[(2a^{2}b^{-1})(-a^{-3}b^{2}) = (-a^{-3}2a^{2})(b^{-1}b^{2}) = -2a^{-1}b\]

Answer 6

oh, i never thought of it that way. So, I can combine same variables together (have the same letter with them), like \[(-a ^{-3} 2a ^{2})\] together in brackets and then simplify them by using exponent laws?

Answer 7

In this case, only because multiplication was the only thing involved so the order of the variables doesn't matter (the commutative property). You still have to follow the various number properties.

Answer 8

ok, so if i have addition in problem i could not do this. but if its multiplication then i can do it , so if i have \[(3u ^{3} v ^{5})(3u ^{2}v)\] i could do the same thing, so i would end up with \[(3u ^{3} 3u ^{2}) (v ^{5} v)\]