## AngelaB97 one year ago how do you rationalize this denominator?

1. AngelaB97

|dw:1441582663963:dw|

2. caominhim

apply the sqaure root to top and bottom

3. caominhim

oh is the the 7th root?

4. caominhim

$\sqrt[7]{\frac{ 1 }{ a^{2} }} = \frac{ \sqrt[7]{1} }{ \sqrt[7]{a^{2}} }$

5. jdoe0001

hmmm how would you rationalize ... say $$\bf \cfrac{1}{a^2}?$$

6. nincompoop

it is up to you $$\huge \frac{1^{\frac{1}{7}}}{(a^2)^\frac{1}{7}}$$

7. AngelaB97

@nincompoop how would you work out the problem further?

8. jdoe0001

by rationalizing, I assume you mean the exponent, as in $$\large a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}$$

9. nincompoop

you can probably make it so there is no root in the denominator

10. AngelaB97

the answer is supposed to be |dw:1441583091798:dw|

11. AngelaB97

i just don't get how

12. nincompoop

mathematicians decided that it is inelegant to have a root in the denominator so we are suppose to stroke their egos

13. nincompoop

so multiply it by 1 that mimics the denominator

14. nincompoop

you know how $$\huge \frac{c}{c} =1$$ or any fraction that has the same numerator and denominator equals 1 with the exception of $$\large \frac{0}{0}$$

15. nincompoop

were you told that's the answer by the book?

16. nincompoop

|dw:1441583625914:dw|

17. nincompoop

|dw:1441583819764:dw|

18. nincompoop

|dw:1441583873041:dw|

19. nincompoop

HELLOOOOOOOOO WHERE ARE YOUUUUUUUUUUUUUUUUU HELLOOOOOOOO ECHOOOOOOO

20. nincompoop

HELLOOOOOOOOO ECHOOOOOOOOO I think you fell into the mathematical abyss or black hole

21. AngelaB97

okay i get what you did

22. AngelaB97

however can you explain why the book only put the rad over the denominator and not the numerator...this is regarding the picute i attached up there

23. nincompoop

i do not see it

24. AngelaB97

|dw:1441588006576:dw|

25. AngelaB97

why did they not put the rad sign over the 1 as well?

26. nincompoop

$$\huge 1^\frac{1}{7} = 1$$

27. nincompoop

the 7th root of 1 is 1 that is why

28. AngelaB97

how I'm so sorry

29. nincompoop

what is the square root of 1 ?

30. AngelaB97

1

31. nincompoop

what is the cube root of 1?

32. nincompoop

also 1

33. nincompoop

the trend follows

34. AngelaB97

so anything to the nth root of 1 is 1

35. nincompoop

nth root providing it is a positive whole number, pretty much

36. nincompoop

I may need an actual mathematician to confirm this with proof, but that is what I know even tho I am not a mathematician

37. AngelaB97

okay well thanks so much for your help! :)

38. nincompoop

no problem enjoy learning

39. AngelaB97

thanks!