## anonymous 5 years ago how do i solve these kinds of problems? x 3/2 = 64

1. anonymous

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

2. asnaseer

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

3. anonymous

yes

4. asnaseer

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

5. anonymous

ok

6. asnaseer

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

7. asnaseer

now:$64=2^6$

8. asnaseer

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

9. anonymous

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

10. asnaseer

ok

11. asnaseer

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

12. anonymous

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

13. asnaseer

$64=2^6$therefore:$64^2=(2^6)^2=2^{12}$

14. asnaseer

do you understand?

15. anonymous

no. 'im still trying to understand the squared part

16. asnaseer

ok, you agree:$64=2^6$

17. anonymous

ok

18. asnaseer

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

19. asnaseer

making sense?

20. anonymous

sort of

21. anonymous

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

22. asnaseer

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

23. anonymous

yes

24. anonymous

but i just learned it, not a pro yet

25. asnaseer

:)

26. asnaseer

ok, lets try a different approach...

27. anonymous

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

28. asnaseer

$64=2^6$so we can write:$64^p=(64)^p=(2^6)^p=2^{6p}$

29. asnaseer

in our case p=2

30. asnaseer

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

31. asnaseer

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

32. anonymous

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

33. asnaseer

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

34. asnaseer

ok, so lets review our last step...

35. anonymous

ok

36. asnaseer

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

37. anonymous

yes

38. asnaseer

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

39. anonymous

hold on..

40. anonymous

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

41. asnaseer

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

42. anonymous

yes well you explained it great, thanks

43. asnaseer

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

44. anonymous

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

45. asnaseer

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

46. asnaseer

*able (not enable)

47. anonymous

gotcha... thanks again :)