anonymous
  • anonymous
x^-2+x^-4= I got x^1/2+x^1/4 but i dont remember the rules well for exponents
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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freckles
  • freckles
x^(-2) doesn't mean x^(1/2) though you can write x^(-2) as 1/x^2
freckles
  • freckles
and same for the x^(-4) this is not x^(1/4)
anonymous
  • anonymous
ohhh okay so do i multiply the exponents?

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Jhannybean
  • Jhannybean
\[x^{-2} -x^{-4}\] You're just looking to factor out this function?
anonymous
  • anonymous
well for the exponents, it says to put it in A/B
Jhannybean
  • Jhannybean
Oh okay, so as @freckles mentioned :)
Jhannybean
  • Jhannybean
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 \(x^{-2} + x^{-4}\)*
anonymous
  • anonymous
i got that now! so do we multiply the exponents to get 1/x^8?
anonymous
  • anonymous
i completely forgot the rules
anonymous
  • anonymous
then how?
Jhannybean
  • Jhannybean
All we can do now, is factor out the denominator.
freckles
  • freckles
\[x^{-2}+x^{-4}=\frac{1}{x^2}+\frac{1}{x^4}\] you can combine the fractions by finding a common denominator
Jhannybean
  • Jhannybean
D'oh!
Jhannybean
  • Jhannybean
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.
Jhannybean
  • Jhannybean
From what @freckles wrote, just find the greatest common denominator between \(x^2\) and \(x^4\).
anonymous
  • anonymous
?
anonymous
  • anonymous
common denominator is x^4?
freckles
  • freckles
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
anonymous
  • anonymous
so itll be x^2/x^4 do i reduce?
freckles
  • freckles
you will have \[\frac{x^2+1}{x^4}\]
anonymous
  • anonymous
wouldnt that equal to x+1/x^2
freckles
  • freckles
no just (x^2+1)/x^4 can't be reduced because you don't have all terms with factor x^2
anonymous
  • anonymous
than would A/B be 2/4? cause the question asked put the exponents as A/B
freckles
  • freckles
what?
freckles
  • freckles
are you saying we are suppose to write in x^(A/B) form?
anonymous
  • anonymous
yes
freckles
  • freckles
\[x^{-2}+x^{-4}=x^{\frac{-2}{1}}+x^{\frac{-4}{1}}\] there is both terms written in x^(A/B) form
anonymous
  • anonymous
oh okay thats easier to understand
anonymous
  • anonymous
then would it be -6
freckles
  • freckles
I don't get your question can you post your whole question
anonymous
  • anonymous
simplofy the rational expression in the form of A/B. x^-2+x^-4
freckles
  • freckles
oh in the form A/B well we did that \[\frac{x^2+1}{x^4} \\ \text{ we have } A=x^2+1 \text{ and } B=x^4\]
anonymous
  • anonymous
oh my god thank you!
freckles
  • freckles
np

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