Question

x^-2+x^-4=
I got x^1/2+x^1/4 but i dont remember the rules well for exponents

Answer 1

x^(-2) doesn't mean x^(1/2)

though you can write x^(-2) as 1/x^2

Answer 2

and same for the x^(-4) this is not x^(1/4)

Answer 3

ohhh okay so do i multiply the exponents?

Answer 4

\[x^{-2} -x^{-4}\] You're just looking to factor out this function?

Answer 5

well for the exponents, it says to put it in A/B

Answer 6

Oh okay, so as @freckles mentioned :)

Answer 7

Recall that \(x^{-\#} \iff \dfrac{1}{x^{\#}}\)

Therefore we can write our function over 1 to make the exponents of the variables positive :)

and i made a typo, my function should have read \(x^{-2} + x^{-4}\)*

Answer 8

i got that now! so do we multiply the exponents to get 1/x^8?

Answer 9

i completely forgot the rules

Answer 10

then how?

Answer 11

All we can do now, is factor out the denominator.

Answer 12

\[x^{-2}+x^{-4}=\frac{1}{x^2}+\frac{1}{x^4}\]
you can combine the fractions by finding a common denominator

Answer 13

D'oh!

Answer 14

I made a really big error. My mistake was in putting the function as a whole in the denominator. In order to turn each variable positive, you must treat each variable as a separate function.

Answer 15

From what @freckles wrote, just find the greatest common denominator between \(x^2\) and \(x^4\).

Answer 16

?

Answer 17

common denominator is x^4?

Answer 18

that is right
\[x^{-2}+x^{-4} \\ \frac{1}{x^2}+\frac{1}{x^4} \\ \frac{1(x^2)}{x^2(x^2)}+\frac{1}{x^4}\]
now you have the same denominator
combine the fractions

Answer 19

so itll be x^2/x^4
do i reduce?

Answer 20

you will have
\[\frac{x^2+1}{x^4}\]

Answer 21

wouldnt that equal to x+1/x^2

Answer 22

no just (x^2+1)/x^4
can't be reduced because you don't have all terms with factor x^2

Answer 23

than would A/B be 2/4? cause the question asked put the exponents as A/B

Answer 24

what?

Answer 25

are you saying we are suppose to write in x^(A/B) form?

Answer 26

yes

Answer 27

\[x^{-2}+x^{-4}=x^{\frac{-2}{1}}+x^{\frac{-4}{1}}\]
there is both terms written in x^(A/B) form

Answer 28

oh okay thats easier to understand

Answer 29

then would it be -6

Answer 30

I don't get your question
can you post your whole question

Answer 31

simplofy the rational expression in the form of A/B. x^-2+x^-4

Answer 32

oh in the form A/B
well we did that
\[\frac{x^2+1}{x^4} \\ \text{ we have } A=x^2+1 \text{ and } B=x^4\]

Answer 33

oh my god thank you!

Answer 34

np