This was taken from a math contest a few months ago.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

x^{x}*y^{y}=z^{z}

find z if:

x=2^{8}* 3^{8}

y=2^{12}* 3^{6}

2. Relevant equations

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

3. The attempt at a solution

Dont even think about calculator

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

or 2^{49268736}* 3^{31352832}

How do you get z alone?

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# Homework Help: Prime factorization, Exponents

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