Solve the equation with rational exponents.

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Solve the equation with rational exponents.

Mathematics
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(x-6) ^3/2 =27
I dont remember how to do this..
\[\large (x-6) ^{\frac{3}{2}} =27\] yes?

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Other answers:

Yeah
because \(\large n^\frac{a}{b} = n^{\frac{a}{1}\times \frac{1}{b}} = (n^a)^{\frac{1}{b}} = (n^{\frac{1}{b}})^a\)
Um okay?
or if its simpler https://gyazo.com/dfe8c6b9853179633b8a8fe3a0bcb746
so in \[\frac{3}{2}\] you have a cube and a square root you want to undo them both, but one by one
\[n^{3/2} = (n^{1/2})^3 = (n^3)^{1/2}\]
and here \(n = x-6\) !!
Um all im really understanding is that n= x-6 ... Except I dont get the point of n
it is an attempt to simplify but it might just be doing the opposite you know that \[n^{1/2} = \sqrt{n}\] yes?
Yes
and \[n^{3/2} = (n^{1/2})^3\] yes
That I dont remember
I thought im suppose to flip 3/2 to 2/3 to cancel it out and put 2/3 by the 27...
if that's how you see it, go for it. it is how you solve it.
Okay. But I dont remember what to do after that
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?
Um its like the reciprocal of 3/2
\[n^{2/3} = (n^2)^{1/3} = \sqrt[3]{n^2}\] and \[n^{2/3} = (n^{1/3})^{2} = (\sqrt[3]{n})^2\]
Okay so your saying... x-6= ^3 square root 27 ^2
sorry, don't really get that notation, just feel free to post what you think the answer is
|dw:1440786073328:dw|
looks good
Okay.. Im stuck there
https://www.google.co.uk/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=calculator
|dw:1440786180440:dw|
?? Nothing is there.. Just a 0
|dw:1440786213763:dw|
729
yes, now cube root of that
Um?
https://gyazo.com/3110dd44529fb9f72a87b50ae9e8e75c
https://gyazo.com/cacad2370ac356783aa9f6f37bf6af73
if you struggle with the idea of a cube root, i would strongly advise you go back over that before trying to solve these
did you see how i made the calculator give us the cube root? \[\large 729^{(1 \ divided \ by\ 3)}\]
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.
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?
So. x-6=9 ?
yes
Okay... Ive been using this as an example. https://www.youtube.com/watch?v=6Y-3mQkqEOA
x=15
yes
Okay. Im still confused but okay. Thanks
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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