I have two very large primes (a, b) , each raised to a large (non-prime) integer powers (p,q) .

I want to evaluate the comparison:

a^p >= b^q

However, I don't want to attempt to calculate a^p, b^q since the results will be astronomically huge, and I only need to know which is the largest.

Obviously if a>b and p>q then the answer is trivial, however in the general case I'm stumped...

Any suggestions ?