how do i solve these kinds of problems?
x 3/2 = 64

- anonymous

how do i solve these kinds of problems?
x 3/2 = 64

- katieb

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- anonymous

on my paper it looks like x with exponent 3 and exponent 2 = 64.... not sure how to put that on here

- asnaseer

\[x^{\frac{3}{2}}=64\]is that right?

- anonymous

yes

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## More answers

- asnaseer

ok, firstly note that \(x^{\frac{1}{2}}\) means square root of x

- anonymous

ok

- asnaseer

so if we square both sides we get:\[(x^{\frac{3}{2}})^2=64^2\]therefore:\[x^3=64^2\]

- asnaseer

now:\[64=2^6\]

- asnaseer

so we can write this as:\[x^3=64^2=(2^6)^2=2^{12}\]

- anonymous

wait i got confused, let me look at what you put

- asnaseer

ok

- asnaseer

I am using the rule:\[(x^a)^b=x^{ab}\]

- anonymous

why is 64 squared 2 to 6th and not just 8?

- asnaseer

\[64=2^6\]therefore:\[64^2=(2^6)^2=2^{12}\]

- asnaseer

do you understand?

- anonymous

no. 'im still trying to understand the squared part

- asnaseer

ok, you agree:\[64=2^6\]

- anonymous

ok

- asnaseer

so we can substitute \(2^6\) where ever we see 64. so we can write:\[64^2=(64)^2=(2^6)^2=2^{12}\]

- asnaseer

making sense?

- anonymous

sort of

- anonymous

i mean i understand the substituting part but i still dont understand the 64 squared = 2 to the 12th

- asnaseer

are you familiar with the rule:\[(x^a)^b=x^{ab}\]

- anonymous

yes

- anonymous

but i just learned it, not a pro yet

- asnaseer

:)

- asnaseer

ok, lets try a different approach...

- anonymous

ok, im sorry and thank you for being patient with me

- asnaseer

\[64=2^6\]so we can write:\[64^p=(64)^p=(2^6)^p=2^{6p}\]

- asnaseer

in our case p=2

- asnaseer

we could also have written it as:\[64=8^2\]therefore:\[64^2=(8^2)^2=8^4\]

- asnaseer

and then used:\[8=2^3\]therefore:\[64^2=8^4=(8)^4=(2^3)^4=2^{12}\]

- anonymous

aha, and 8 to the 4th is the same as 2 to the 12th....ok got it now

- asnaseer

yes - well done - I think the fog is beginning to clear :-)

- asnaseer

ok, so lets review our last step...

- anonymous

ok

- asnaseer

we got to:\[x^3=64^2=(2^6)^2=2^{12}\]this should now be clear - yes?

- anonymous

yes

- asnaseer

ok, so next we take cube roots of both sides to get:\[(x^3)^{\frac{1}{3}}=(2^{12})^{\frac{1}{3}}\]therefore:\[x=2^4=16\]

- anonymous

hold on..

- anonymous

ok, i was doing the calculating to follow along with you

- asnaseer

no problem - the main thing is to ensure you understand the concepts

- anonymous

yes well you explained it great, thanks

- asnaseer

you are very welcome.
is it all clear now or did you want more explanation?

- anonymous

i think i got it now, i was just stuck on the squared part. makes sense now. Thank you very much

- asnaseer

ok - I'm glad I was enable to assist you in your mathematical quest :p - all the best...

- asnaseer

*able (not enable)

- anonymous

gotcha... thanks again :)

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