# Prime factorization, Exponents

This was taken from a math contest a few months ago.

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

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?

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