# Prime factorization, Exponents

1. Mar 25, 2007

### turdferguson

This was taken from a math contest a few months ago.
1. The problem statement, all variables and given/known data
xx*yy=zz

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

2. Relevant equations
Theres undoubtably some trick, but I have yet to find it

3. The attempt at a solution

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?

2. Mar 25, 2007

### Werg22

$$z^{z} = 2^{2^{11}*3^{7}*11} * 3^{2^{11}*3^{7}*7} = ({2^{11}})^{2^{11}*3^{7}}*({3^{7}})^{2^{11}*3^{7}} = ({2^{11}*3^{7}})^{2^{11}*3^{7}}$$

$$z = {2^{11}*3^{7}}$$

Last edited: Mar 25, 2007