Destinyyyy
  • Destinyyyy
Solve the equation with rational exponents.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Destinyyyy
  • Destinyyyy
(x-6) ^3/2 =27
Destinyyyy
  • Destinyyyy
I dont remember how to do this..
IrishBoy123
  • IrishBoy123
\[\large (x-6) ^{\frac{3}{2}} =27\] yes?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Destinyyyy
  • Destinyyyy
Yeah
IrishBoy123
  • 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
  • Destinyyyy
Um okay?
IrishBoy123
  • IrishBoy123
or if its simpler https://gyazo.com/dfe8c6b9853179633b8a8fe3a0bcb746
IrishBoy123
  • 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
  • IrishBoy123
\[n^{3/2} = (n^{1/2})^3 = (n^3)^{1/2}\]
IrishBoy123
  • IrishBoy123
and here \(n = x-6\) !!
Destinyyyy
  • Destinyyyy
Um all im really understanding is that n= x-6 ... Except I dont get the point of n
IrishBoy123
  • 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
  • Destinyyyy
Yes
IrishBoy123
  • IrishBoy123
and \[n^{3/2} = (n^{1/2})^3\] yes
Destinyyyy
  • Destinyyyy
That I dont remember
Destinyyyy
  • Destinyyyy
I thought im suppose to flip 3/2 to 2/3 to cancel it out and put 2/3 by the 27...
IrishBoy123
  • IrishBoy123
if that's how you see it, go for it. it is how you solve it.
Destinyyyy
  • Destinyyyy
Okay. But I dont remember what to do after that
IrishBoy123
  • 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
  • Destinyyyy
Um its like the reciprocal of 3/2
IrishBoy123
  • 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
  • Destinyyyy
Okay so your saying... x-6= ^3 square root 27 ^2
IrishBoy123
  • IrishBoy123
sorry, don't really get that notation, just feel free to post what you think the answer is
Destinyyyy
  • Destinyyyy
|dw:1440786073328:dw|
IrishBoy123
  • IrishBoy123
looks good
Destinyyyy
  • Destinyyyy
Okay.. Im stuck there
IrishBoy123
  • IrishBoy123
https://www.google.co.uk/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=calculator
IrishBoy123
  • IrishBoy123
|dw:1440786180440:dw|
Destinyyyy
  • Destinyyyy
?? Nothing is there.. Just a 0
IrishBoy123
  • IrishBoy123
|dw:1440786213763:dw|
Destinyyyy
  • Destinyyyy
729
IrishBoy123
  • IrishBoy123
yes, now cube root of that
Destinyyyy
  • Destinyyyy
Um?
IrishBoy123
  • IrishBoy123
https://gyazo.com/3110dd44529fb9f72a87b50ae9e8e75c
IrishBoy123
  • IrishBoy123
https://gyazo.com/cacad2370ac356783aa9f6f37bf6af73
IrishBoy123
  • 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
  • IrishBoy123
did you see how i made the calculator give us the cube root? \[\large 729^{(1 \ divided \ by\ 3)}\]
Destinyyyy
  • 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
  • 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
  • Destinyyyy
So. x-6=9 ?
IrishBoy123
  • IrishBoy123
yes
Destinyyyy
  • Destinyyyy
Okay... Ive been using this as an example. https://www.youtube.com/watch?v=6Y-3mQkqEOA
Destinyyyy
  • Destinyyyy
x=15
IrishBoy123
  • IrishBoy123
yes
Destinyyyy
  • Destinyyyy
Okay. Im still confused but okay. Thanks
IrishBoy123
  • 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!

Looking for something else?

Not the answer you are looking for? Search for more explanations.