Question

Help with negative exponents please:

(c^-1 + d^-1) \ (c^-2 + d^-2)

Answer 1

hint: multiply every term by c^2d^2

Answer 2

I did that and got cd (d + c) \ (d^2 + c^2)...can this be simplified?

Answer 3

I'm getting

\[\large \frac{cd(d+c)}{d^2 + c^2}\]

which is what you have and you can't simplify further

so nice work

Answer 4

thank you so much! are you available to help with another problem?

Answer 5

sure I can do one more

Answer 6

thank you :) (x^-3 + y^-3) \ (x^-1 + y^-1)

Answer 7

multiply everything by x^3y^3 and tell me what you get

Answer 8

(y^3 + x^3) \ x^2y^3

Answer 9

multiply each term by x^3y^3 to get


x^-3 times x^3y^3 = y^3
y^-3 times x^3y^3 = x^3

so that part is correct in the numerator

Answer 10

in the denominator we have

x^-1 times x^3y^3 = x^2y^3
y^-1 times x^3y^3 = x^3y^2

Answer 11

so the final answer is

\[\large \frac{y^3+x^3}{x^2y^3+x^3y^2}\]

and optionally you can factor to get

\[\large \frac{y^3+x^3}{x^2y^2(y+x)}\]

Answer 12

hi @jim_thompson5910 did u get my PM?

Answer 13

oh I guess you can factor the numerator as well to get

y^3 + x^3 = (y+x)(y^2 + yx + x^2)

Answer 14

how do you get the + x^3y^2 in the denominator?

Answer 15

oh i see that in the numerator... would that be the same as (x + y) (x^2 + xy + y^2)?

Answer 16

in the denominator, we have the terms x^-1 + y^-1

multiply those term by x^3y^3 to get x^2y^3+x^3y^2

Answer 17

sorry I see

Answer 18

sorry made a typo, it should be y^3 + x^3 = (y+x)(y^2 - yx + x^2)

Answer 19

so the full step by step picture looks like this

Answer 20

\[\large \frac{x^{-3} + y^{-3}}{x^{-1} + y^{-1}}\]

\[\large \frac{x^3y^3*x^{-3} + x^3y^3*y^{-3}}{x^3y^3*x^{-1} + x^3y^3*y^{-1}}\]

\[\large \frac{y^3+x^3}{x^2y^3+x^3y^2}\]

\[\large \frac{(y+x)(y^2 - yx + x^2)}{x^2y^2(y+x)}\]

\[\large \frac{\cancel{(y+x)}(y^2 - yx + x^2)}{x^2y^2\cancel{(y+x)}}\]

\[\large \frac{y^2 - yx + x^2}{x^2y^2}\]


------------------------------------------------------------------------------------------


Final Answer:

\[\large \frac{y^2 - yx + x^2}{x^2y^2}\]

Answer 21

thank you so much for taking the time to explain it so well!

Answer 22

yw