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

1. freckles

x^(-2) doesn't mean x^(1/2) though you can write x^(-2) as 1/x^2

2. freckles

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

3. anonymous

ohhh okay so do i multiply the exponents?

4. Jhannybean

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

5. anonymous

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

6. Jhannybean

Oh okay, so as @freckles mentioned :)

7. 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 $$x^{-2} + x^{-4}$$*

8. anonymous

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

9. anonymous

i completely forgot the rules

10. anonymous

then how?

11. Jhannybean

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

12. freckles

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

13. Jhannybean

D'oh!

14. 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.

15. Jhannybean

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

16. anonymous

?

17. anonymous

common denominator is x^4?

18. 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

19. anonymous

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

20. freckles

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

21. anonymous

wouldnt that equal to x+1/x^2

22. freckles

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

23. anonymous

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

24. freckles

what?

25. freckles

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

26. anonymous

yes

27. freckles

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

28. anonymous

oh okay thats easier to understand

29. anonymous

then would it be -6

30. freckles

31. anonymous

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

32. freckles

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

33. anonymous

oh my god thank you!

34. freckles

np