Question

simplify : (-xy^3)^2 x^-3

Answer 1

\[(-xy^3)^2 \cdot x^{-3}\] distribute the power of two to all variables inside the parenthesis first.

Answer 2

(-x^2y^6)x^-3

Answer 3

\[[(-x)^2(y^3)^2] \cdot x^{-3}\] Good.:)

Answer 4

I'm not sure what to do next.

Answer 5

\[(-x)^2 = (-x)(-x) = x\]NOw you've got \[(x\cdot y^6) \cdot x^{-3}\]

Answer 6

Now we multiply \(x^{-3}\) into the stuff with parenthesis.

Answer 7

\[(x \cdot x^{-3}) \cdot (y^6 \cdot x^{-3})\]

Answer 8

\[(x \cdot x^{-3}) = x^{1-3} = (x^{-2})\cdot x^{-3}y^6\]

Answer 9

(x^-2)(y^6 x x^-3)

Answer 10

y^6/x

Answer 11

Actually, let's try it another way.

Answer 12

what would you do after that?
multiply the x^-2 times the x^-3?

Answer 13

ok

Answer 14

Say we want to make all the variables positive first. since we have \(x^{-3}\) we can rewrite that as a positive power by putting it over 1. \[\frac{1}{x^3}\]

Answer 15

ok

Answer 16

Now that makes all our variables positive. you could have continued doing it the way we were doing it at first, and still ended up with the same result by making all the negative variables positive at the end, I just thought this second approach might be a bit easier to understand.

Answer 17

so then (-x^2) would be x^2

Answer 18

x^3-x^2

Answer 19

y6/x

Answer 20

So now we have \((-xy^3)\) and \(\frac{1}{x^3}\)

Answer 21

oh yeah, you got it.Good job!

Answer 22

THANK YOU SO MUCH FOR YOUR HELP!

Answer 23

Haha no problem.