Solve the equation with rational exponents.

- Destinyyyy

Solve the equation with rational exponents.

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- Destinyyyy

(x-6) ^3/2 =27

- Destinyyyy

I dont remember how to do this..

- IrishBoy123

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

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## More answers

- Destinyyyy

Yeah

- IrishBoy123

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

- Destinyyyy

Um okay?

- IrishBoy123

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

- IrishBoy123

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

- IrishBoy123

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

- IrishBoy123

and here \(n = x-6\) !!

- Destinyyyy

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

- IrishBoy123

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

- Destinyyyy

Yes

- IrishBoy123

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

- Destinyyyy

That I dont remember

- Destinyyyy

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

- IrishBoy123

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

- Destinyyyy

Okay. But I dont remember what to do after that

- 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?

- Destinyyyy

Um its like the reciprocal of 3/2

- IrishBoy123

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

- Destinyyyy

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

- IrishBoy123

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

- Destinyyyy

|dw:1440786073328:dw|

- IrishBoy123

looks good

- Destinyyyy

Okay.. Im stuck there

- IrishBoy123

https://www.google.co.uk/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=calculator

- IrishBoy123

|dw:1440786180440:dw|

- Destinyyyy

?? Nothing is there.. Just a 0

- IrishBoy123

|dw:1440786213763:dw|

- Destinyyyy

729

- IrishBoy123

yes, now cube root of that

- Destinyyyy

Um?

- IrishBoy123

https://gyazo.com/3110dd44529fb9f72a87b50ae9e8e75c

- IrishBoy123

https://gyazo.com/cacad2370ac356783aa9f6f37bf6af73

- 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

- IrishBoy123

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

- 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.

- 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?

- Destinyyyy

So.
x-6=9 ?

- IrishBoy123

yes

- Destinyyyy

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

- Destinyyyy

x=15

- IrishBoy123

yes

- Destinyyyy

Okay. Im still confused but okay. Thanks

- 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!

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