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OfflineHelixx
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Math
    #9341753 - 12/01/08 01:20 AM (15 years, 3 months ago)

Wondering if anyone is good at math that can help me with two basic problems..

Writing each expression as a positive exponent and then simplifying.

12 ^ -3/4

and

(-27) ^ -2/3

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OfflineCoaster
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Re: Math [Re: Helixx]
    #9341774 - 12/01/08 01:26 AM (15 years, 3 months ago)

1                        1
-----------            --
2(108)^(1/4)            9


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OfflineCepheus
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Re: Math [Re: Helixx]
    #9341779 - 12/01/08 01:26 AM (15 years, 3 months ago)

12^-3/4 = 1/((12^3)^1/4)

one over the 4th root of 12 cubed .. don't think you can simplify that any further :shrug:.

(-27)^-2/3 = 1/9


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OfflineHelixx
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Re: Math [Re: Cepheus]
    #9341813 - 12/01/08 01:34 AM (15 years, 3 months ago)

Thanks.  Is there an easy process to do these?  I can't seem to find the chapter in my math book

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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
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Re: Math [Re: Helixx]
    #9341817 - 12/01/08 01:35 AM (15 years, 3 months ago)

Formula: 0

= 0.1551008098503499331568697911638723479585340376129420625156627518464939023326\
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187774416055800494...

Edited by isaacein (12/01/08 01:39 AM)

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OfflineCoaster
Baʿal
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Registered: 05/22/06
Posts: 33,501
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Re: Math [Re: Helixx]
    #9341820 - 12/01/08 01:36 AM (15 years, 3 months ago)

Quote:

Helixx said:
Thanks.  Is there an easy process to do these?  I can't seem to find the chapter in my math book



u thank him grrrr

lol


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OfflineHelixx
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Re: Math [Re: Coaster]
    #9341828 - 12/01/08 01:38 AM (15 years, 3 months ago)

Heh i use quick reply, it was thanks to both of you

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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
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Re: Math [Re: Helixx]
    #9341856 - 12/01/08 01:43 AM (15 years, 3 months ago)

Here are the first 1000 numbers in the continued fraction expansion of (12)^(-3/4).

{0, 6, 2, 4, 3, 1, 12, 1, 3, 2, 1, 3, 1, 1, 1, 2, 1, 17, 1, 1, 1, 3, 2, 1, 1, \
3, 1, 1, 2, 2, 1, 8, 2, 19, 4, 2, 1, 5, 1, 1, 2, 1, 1, 1, 2, 64, 1, 192, 1, \
76, 1, 1, 1, 1, 5, 4, 2, 1, 1, 12, 1, 1, 31, 4, 1, 3, 1, 1, 5, 5, 1, 23, 1, \
4, 1, 3, 10, 1, 3, 10, 1, 8, 1, 2, 1, 11, 1, 1, 2, 2, 1, 1, 4, 1, 6, 16, 2, \
4, 2, 1, 2, 1, 2, 1, 1, 2, 7, 12, 3, 1, 2, 4, 1, 2, 4, 110, 11, 2, 2, 7, 2, \
21, 1, 4, 3, 1, 1, 3, 2, 3, 2, 10, 1, 1, 1, 11, 1, 1, 2, 13, 1, 4, 3, 2, 1, \
2, 1, 4, 1, 3, 2, 2, 1, 5, 1, 3, 19, 16, 2, 7, 2, 2, 10, 2, 15, 2, 1, 3, 4, \
1, 1, 1, 13, 1, 5, 1, 1, 4, 8, 6, 6, 3, 1, 30, 42, 1, 6, 1, 1, 11, 1, 3, 1, \
6, 1, 9, 1, 3, 2, 4, 1, 5, 2, 2, 7, 2, 1, 1, 4, 3, 1, 3, 24, 1, 5, 4, 2, 1, \
2, 2, 1, 1, 1, 3, 1, 1, 2, 47, 1, 5, 1, 3, 4, 2, 1, 1, 1, 1, 24, 5, 6, 10, 2, \
1, 5, 1, 1, 5, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 7, 10, 1, 6, 1, 2, 1, 4, 1, 2, \
1, 12, 1, 3, 1, 6, 1, 1, 5, 1, 6, 4, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 5, 1, 4, \
2, 1, 3, 1, 1, 1, 1, 1, 9, 1, 2, 1, 1, 1, 4, 8, 1, 35, 17, 1, 129, 1, 1, 1, \
19, 2, 5, 3, 1, 4, 1, 1, 1, 1, 20, 4, 1, 2, 6, 9, 2, 1, 5, 4, 35, 1, 3, 8, 7, \
1, 1, 1, 9, 2, 7, 3, 1, 2, 1, 4, 2, 6, 2, 2, 3, 58, 3, 1, 1, 140, 5, 1, 5, 1, \
1, 1, 4, 1, 1, 1, 2, 6, 5, 10, 54, 6, 2, 1, 1, 33, 1, 1, 7, 1, 1, 10, 7, 3, \
47, 4, 1, 3, 2, 3, 1, 17, 2, 1, 3, 4, 2, 1, 4, 2, 9, 3, 4, 3, 1, 17, 1, 2, 3, \
3, 1, 1, 3, 1, 2, 5, 3, 3, 2, 3, 2, 88, 1, 44, 1, 3, 2, 4, 2, 3, 38, 9, 1, 2, \
1, 1, 2, 1, 4, 1, 1, 2, 1, 3, 1, 4, 1, 3, 4, 3, 1, 2, 2, 2, 1, 9, 1, 4, 3, 2, \
3, 1, 2, 2, 2, 1, 1, 14, 1, 1, 7, 1, 4, 1, 1, 1, 46, 7, 1, 27, 3, 1, 4, 1, 5, \
2, 60, 1, 10, 1, 2, 1, 1, 6, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 2, 1, 1, \
3, 1, 1, 6, 1, 2, 7, 15, 3, 10, 1, 3, 1, 2, 2, 1, 2, 4, 528, 1, 3, 3, 9, 1, \
9, 1, 1, 3, 1, 3, 1, 10, 2, 1, 2, 1, 1, 2, 5, 2, 4, 1, 40, 1, 2, 1, 41, 16, \
1, 102, 1, 2, 2, 4, 1, 4, 18, 1, 2, 2, 3, 1, 3, 17, 1, 6, 1, 3, 1, 8, 2, 11, \
1, 1, 28, 3, 1, 1, 1, 19, 2, 1, 46, 1, 1, 2, 4, 13, 12, 1, 3, 1, 1, 3, 2, 1, \
3, 3, 2, 2, 5, 11, 5, 1, 1, 3, 38, 1, 4, 15, 1, 1, 2, 1, 3, 1, 1, 3, 16, 1, \
3, 9, 3, 1, 6, 3, 7, 1, 9, 2, 1, 1, 1, 1, 47, 1, 10, 16, 1, 8, 1, 2, 1, 2, 1, \
2, 2, 2, 2, 1, 3, 5, 1, 10, 5, 1, 2, 8, 1, 18, 5, 1, 7, 1, 6, 2, 2, 1, 38, 1, \
1, 27, 2, 8, 2, 2, 52, 1, 5, 3, 12, 2, 2, 3, 1, 1, 3, 2, 2, 2, 2, 1, 1, 2, 3, \
2, 4, 1, 22, 1, 17, 5, 4, 3, 28, 1, 5, 1, 3, 22, 1, 1, 1, 1, 1, 1, 1, 25, 4, \
1, 2, 1, 10, 1, 1, 2, 40, 1, 12, 1, 2, 1, 2, 1, 2, 2, 1, 3, 2, 1, 153, 5, 1, \
7, 10, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 1, 1, 4, 1, 2, 2, 2, 1, 3, 8, 1, 3, 1, \
29, 1, 31, 1, 3, 1, 1, 3, 2, 1, 77, 4, 1, 1, 1, 1, 6, 2, 2, 1, 5, 22, 1, 4, \
144, 3, 53, 1, 3, 4, 1, 1, 1, 2, 1, 8, 62, 4, 1, 2, 1, 5, 1, 11, 69, 6, 1, 2, \
4, 2, 1, 3, 30, 1, 2, 1, 2, 1, 8, 2, 8, 1, 1, 52, 1, 43, 1, 1, 3, 1, 12, 3, \
1, 1, 2, 4, 4, 1305, 1, 20, 5, 1, 9, 3, 1, 1, 4, 2, 1, 3, 6, 6, 1, 1, 3, 5, \
6, 3, 7, 5, 1, 1, 1, 1, 1, 11, 1, 16, 1, 1, 1, 1, 3, 1, 2, 3, 2, 3, 1, 15, 3, \
2, 1, 2, 45, 7, 4, 1, 7, 2, 14, 1, 4, 1, 72, 1, 1, 5, 1, 47, 1, 22, 138, 9, \
1, 1, 3, 3, 1, 27, 2, 5, 7, 1, 1, 1, 5, 1, 1, 1, 1, 1, 75, 2, 1, 1, 1, 12, 6, \
2, 2, 9, 1, 1, 4, 4, 1, 3, 1, 10, 1, 1, 1, 32, 1, 19, 1, 11, 1, 2, 1, 1, 1, \
20, 1, 3, 4, 2, 3, 1, 1, 1, 1, 7, 2, 8, 1, 2, 1, 1, 7, 1, 1, 1, 1}


--------------------
Formula: 0

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OfflineCoaster
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Re: Math [Re: Helixx]
    #9341858 - 12/01/08 01:44 AM (15 years, 3 months ago)

:vaped:

that floozy isaacein is tryin to make us look bad


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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
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Re: Math [Re: Coaster]
    #9341867 - 12/01/08 01:45 AM (15 years, 3 months ago)

Well no I was just pointing out the way to the answer without a calculator, for the OP.


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OfflineCoaster
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Registered: 05/22/06
Posts: 33,501
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Re: Math [Re: isaacein]
    #9341869 - 12/01/08 01:46 AM (15 years, 3 months ago)

ya man ur killer :thumbup:


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OfflineHelixx
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Re: Math [Re: isaacein]
    #9341870 - 12/01/08 01:46 AM (15 years, 3 months ago)

Teach me how to solve it please :yesnod:

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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 1 month
Re: Math [Re: Coaster]
    #9341885 - 12/01/08 01:53 AM (15 years, 3 months ago)

Quote:

Coaster said:
ya man ur killer :thumbup:




Thanks :cool:

I try to get better though. I wish I had a very good intuition. I have a good imagination for coming up with interesting problems but solving them is of course another thing :smile:

Here's one for you.

Show that if you have a d-dimensional ball of radius 1, then the expected distance between a random point in the ball and the center is Formula: 0


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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 1 month
Re: Math [Re: Helixx]
    #9341892 - 12/01/08 01:56 AM (15 years, 3 months ago)

Well I just factored 12 into prime numbers (Formula: 0) and applied the exponents to the primes (using the basic rules for manipulating exponents : Formula: 1.


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OfflineCoaster
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Re: Math [Re: isaacein]
    #9341897 - 12/01/08 02:00 AM (15 years, 3 months ago)



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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 1 month
Re: Math [Re: Coaster]
    #9341907 - 12/01/08 02:03 AM (15 years, 3 months ago)

Quote:

Coaster said:
canonical factorization




You should give my problem a try! I'll send you a one dollar check for the answer, signed with my real name. It's pretty easy with calculus if you're familiar with probability density functions. Otherwise there are ways to avoid using calculus here but it's not great.


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OfflineCoaster
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Re: Math [Re: isaacein]
    #9341925 - 12/01/08 02:07 AM (15 years, 3 months ago)

so if its a 3-dimensional ball then the distance is 3/4 :confused:


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OfflineNoteworthy
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Re: Math [Re: isaacein]
    #9341932 - 12/01/08 02:09 AM (15 years, 3 months ago)

to try and give the OP a hint at how to do these problems:

first, convert a negative exponent into a positive by making it a fraction

(x^-1) = 1/(x^1)

then split up a fraction exponent into two exponents multiplied

(x^y/z) = (x^y)*(x^1/z)

then convert fraction exponents into surds (in the above case, it would be the 'z' root of x)


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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 1 month
Re: Math [Re: Coaster]
    #9341945 - 12/01/08 02:12 AM (15 years, 3 months ago)

I'll give you another dollar for this one.

Show that if Formula: 0 is the number of prime divisors of n, with Formula: 1, then, as Formula: 2,

Formula: 3

where the sum on the right is extended to all primes <=n.


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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 1 month
Re: Math [Re: Noteworthy]
    #9341957 - 12/01/08 02:14 AM (15 years, 3 months ago)

Yeah that would be the first part, which I skipped.


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