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Prime factorization, Exponents

  • #1
312
0
This was taken from a math contest a few months ago.

Homework Statement


xx*yy=zz

find z if:
x=28 * 38
y=212 * 36

Homework Equations


Theres undoubtably some trick, but I have yet to find it

The Attempt at a Solution


Dont even think about calculator

I showed my math teacher, and he was able to find that zz=2(211*37*11) * 3(211*37*7)

or 249268736 * 331352832

How do you get z alone?
 

Answers and Replies

  • #2
1,425
1
[tex]z^{z} = 2^{2^{11}*3^{7}*11} * 3^{2^{11}*3^{7}*7} = ({2^{11}})^{2^{11}*3^{7}}*({3^{7}})^{2^{11}*3^{7}} = ({2^{11}*3^{7}})^{2^{11}*3^{7}} [/tex]

[tex]z = {2^{11}*3^{7}} [/tex]
 
Last edited:

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