Question

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

Answer 1

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

Answer 2

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

Answer 3

yes

Answer 4

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

Answer 5

ok

Answer 6

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

Answer 7

now:\[64=2^6\]

Answer 8

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

Answer 9

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

Answer 10

ok

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

do you understand?

Answer 15

no. 'im still trying to understand the squared part

Answer 16

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

Answer 17

ok

Answer 18

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

Answer 19

making sense?

Answer 20

sort of

Answer 21

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

Answer 22

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

Answer 23

yes

Answer 24

but i just learned it, not a pro yet

Answer 25

:)

Answer 26

ok, lets try a different approach...

Answer 27

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

Answer 28

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

Answer 29

in our case p=2

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

ok, so lets review our last step...

Answer 35

ok

Answer 36

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

Answer 37

yes

Answer 38

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

Answer 39

hold on..

Answer 40

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

Answer 41

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

Answer 42

yes well you explained it great, thanks

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

*able (not enable)

Answer 47

gotcha... thanks again :)