Question

Is anyone available to help with rewriting negative exponents?

Answer 1

Only if you write the problem statement and demonstrate your best work.

Answer 2

i will :)

Answer 3

x^-2 - y^-2 \ x^-3 + y^-3

Answer 4

Wish I could read that. Should it say \(\dfrac{x^{-2} - y^{-2}}{x^{-3} + y^{-3}}\)? It doesn't say that at all. I'm totally guessing.

Answer 5

the negative exponents on the bottom should be 3

Answer 6

Which they are. If that is what you intended, you should have written this:

(x^-2 - y^-2) / (x^-3 + y^-3)

What a difference parentheses can make!

Answer 7

ok thank you :)

Answer 8

IF it were me, I would multiply both numerator and denominator by x^3.

Answer 9

i tried multiplying the numerator and denominator by x^3y^3 and ended up with (xy^3 - x^3y) / (y^3 + x^3) but not sure if this is correct, and then how to simplify

Answer 10

Give that another try. You should get:

\(\dfrac{x - x^{3}y^{-2}}{1 + x^{3}y^{-3}}\)

There should not yet be any positive y exponents.

Answer 11

the assignment is to rewrite the expression so that there are only positive exponents and then simplify

Answer 12

Whoops. I see you jumped ahead of me. So now you have:

\(\dfrac{xy^{3} - yx^{3}}{y^{3} + x^{3}}\)

Answer 13

Okay, now it's time to see if we can factor anything.

The numerator looks easy enough: xy(y^2 - x^2) = xy(x+y)(x-y)

Do you see all that?

Answer 14

thank you, yes i see that

Answer 15

can the denominator be factored?

Answer 16

This is a great secret.

Remember that a difference of SQUARES can be factored but a SUM of squares cannot!
This is not so for cubes. Both a SUM and a DIFFERENCE can be factored.

\(y^{3} + x^{3} = (y+x)(y^{2} - yx + x^{2})\)
\(y^{3} - x^{3} = (y+x)(y^{2} + yx + x^{2})\)

Answer 17

thank you so much:) would you be willing to walk through another problem with me?

Answer 18

Post on a separate thread, please. I still have a few minutes.

Answer 19

k thank you