## Destinyyyy one year ago Solve the equation with rational exponents.

1. Destinyyyy

(x-6) ^3/2 =27

2. Destinyyyy

I dont remember how to do this..

3. IrishBoy123

$\large (x-6) ^{\frac{3}{2}} =27$ yes?

4. Destinyyyy

Yeah

5. IrishBoy123

because $$\large n^\frac{a}{b} = n^{\frac{a}{1}\times \frac{1}{b}} = (n^a)^{\frac{1}{b}} = (n^{\frac{1}{b}})^a$$

6. Destinyyyy

Um okay?

7. IrishBoy123

or if its simpler https://gyazo.com/dfe8c6b9853179633b8a8fe3a0bcb746

8. IrishBoy123

so in $\frac{3}{2}$ you have a cube and a square root you want to undo them both, but one by one

9. IrishBoy123

$n^{3/2} = (n^{1/2})^3 = (n^3)^{1/2}$

10. IrishBoy123

and here $$n = x-6$$ !!

11. Destinyyyy

Um all im really understanding is that n= x-6 ... Except I dont get the point of n

12. IrishBoy123

it is an attempt to simplify but it might just be doing the opposite you know that $n^{1/2} = \sqrt{n}$ yes?

13. Destinyyyy

Yes

14. IrishBoy123

and $n^{3/2} = (n^{1/2})^3$ yes

15. Destinyyyy

That I dont remember

16. Destinyyyy

I thought im suppose to flip 3/2 to 2/3 to cancel it out and put 2/3 by the 27...

17. IrishBoy123

if that's how you see it, go for it. it is how you solve it.

18. Destinyyyy

Okay. But I dont remember what to do after that

19. IrishBoy123

well, that is what i am trying to get at. you now have $x - 6 = 27^{\frac{2}{3}}$ but do you know what that 2/3 actually means?

20. Destinyyyy

Um its like the reciprocal of 3/2

21. IrishBoy123

$n^{2/3} = (n^2)^{1/3} = \sqrt[3]{n^2}$ and $n^{2/3} = (n^{1/3})^{2} = (\sqrt[3]{n})^2$

22. Destinyyyy

Okay so your saying... x-6= ^3 square root 27 ^2

23. IrishBoy123

sorry, don't really get that notation, just feel free to post what you think the answer is

24. Destinyyyy

|dw:1440786073328:dw|

25. IrishBoy123

looks good

26. Destinyyyy

Okay.. Im stuck there

27. IrishBoy123
28. IrishBoy123

|dw:1440786180440:dw|

29. Destinyyyy

?? Nothing is there.. Just a 0

30. IrishBoy123

|dw:1440786213763:dw|

31. Destinyyyy

729

32. IrishBoy123

yes, now cube root of that

33. Destinyyyy

Um?

34. IrishBoy123
35. IrishBoy123
36. IrishBoy123

if you struggle with the idea of a cube root, i would strongly advise you go back over that before trying to solve these

37. IrishBoy123

did you see how i made the calculator give us the cube root? $\large 729^{(1 \ divided \ by\ 3)}$

38. Destinyyyy

Yeah but that doesnt help me.. I dont know how to do that on my calculator. And I dont remember doing that when I was solving this last term.

39. IrishBoy123

you may see that doing this the other way round is easier |dw:1440786735885:dw| recommend: A) look at these https://gyazo.com/827f7854b216732ea2587538a9759ba0 the 2 fractional exponents at the bottom, that's basically what we are doing B) play with your calculator ----- now we know we are looking for 9 so can you finish off for x?

40. Destinyyyy

So. x-6=9 ?

41. IrishBoy123

yes

42. Destinyyyy

Okay... Ive been using this as an example. https://www.youtube.com/watch?v=6Y-3mQkqEOA

43. Destinyyyy

x=15

44. IrishBoy123

yes

45. Destinyyyy

Okay. Im still confused but okay. Thanks

46. IrishBoy123

really not sure that video is any good, it's all over the place. maybe go to the math is fun thing i linked and they have worked examples too. try to understand the exponents rules and how they work. get a feel for it rather than just flipping rational exponents over the place. good luck!