anonymous
  • anonymous
how do i solve these kinds of problems? x 3/2 = 64
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
on my paper it looks like x with exponent 3 and exponent 2 = 64.... not sure how to put that on here
asnaseer
  • asnaseer
\[x^{\frac{3}{2}}=64\]is that right?
anonymous
  • anonymous
yes

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asnaseer
  • asnaseer
ok, firstly note that \(x^{\frac{1}{2}}\) means square root of x
anonymous
  • anonymous
ok
asnaseer
  • asnaseer
so if we square both sides we get:\[(x^{\frac{3}{2}})^2=64^2\]therefore:\[x^3=64^2\]
asnaseer
  • asnaseer
now:\[64=2^6\]
asnaseer
  • asnaseer
so we can write this as:\[x^3=64^2=(2^6)^2=2^{12}\]
anonymous
  • anonymous
wait i got confused, let me look at what you put
asnaseer
  • asnaseer
ok
asnaseer
  • asnaseer
I am using the rule:\[(x^a)^b=x^{ab}\]
anonymous
  • anonymous
why is 64 squared 2 to 6th and not just 8?
asnaseer
  • asnaseer
\[64=2^6\]therefore:\[64^2=(2^6)^2=2^{12}\]
asnaseer
  • asnaseer
do you understand?
anonymous
  • anonymous
no. 'im still trying to understand the squared part
asnaseer
  • asnaseer
ok, you agree:\[64=2^6\]
anonymous
  • anonymous
ok
asnaseer
  • 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
  • asnaseer
making sense?
anonymous
  • anonymous
sort of
anonymous
  • anonymous
i mean i understand the substituting part but i still dont understand the 64 squared = 2 to the 12th
asnaseer
  • asnaseer
are you familiar with the rule:\[(x^a)^b=x^{ab}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
but i just learned it, not a pro yet
asnaseer
  • asnaseer
:)
asnaseer
  • asnaseer
ok, lets try a different approach...
anonymous
  • anonymous
ok, im sorry and thank you for being patient with me
asnaseer
  • asnaseer
\[64=2^6\]so we can write:\[64^p=(64)^p=(2^6)^p=2^{6p}\]
asnaseer
  • asnaseer
in our case p=2
asnaseer
  • asnaseer
we could also have written it as:\[64=8^2\]therefore:\[64^2=(8^2)^2=8^4\]
asnaseer
  • asnaseer
and then used:\[8=2^3\]therefore:\[64^2=8^4=(8)^4=(2^3)^4=2^{12}\]
anonymous
  • anonymous
aha, and 8 to the 4th is the same as 2 to the 12th....ok got it now
asnaseer
  • asnaseer
yes - well done - I think the fog is beginning to clear :-)
asnaseer
  • asnaseer
ok, so lets review our last step...
anonymous
  • anonymous
ok
asnaseer
  • asnaseer
we got to:\[x^3=64^2=(2^6)^2=2^{12}\]this should now be clear - yes?
anonymous
  • anonymous
yes
asnaseer
  • 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
  • anonymous
hold on..
anonymous
  • anonymous
ok, i was doing the calculating to follow along with you
asnaseer
  • asnaseer
no problem - the main thing is to ensure you understand the concepts
anonymous
  • anonymous
yes well you explained it great, thanks
asnaseer
  • asnaseer
you are very welcome. is it all clear now or did you want more explanation?
anonymous
  • anonymous
i think i got it now, i was just stuck on the squared part. makes sense now. Thank you very much
asnaseer
  • asnaseer
ok - I'm glad I was enable to assist you in your mathematical quest :p - all the best...
asnaseer
  • asnaseer
*able (not enable)
anonymous
  • anonymous
gotcha... thanks again :)

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