Hey guys,
I know this one is pretty well explained in the linked thread, but since it's here I want to make one major point.
With exponent rules, you have to have either the same base or the same exponent to be able to apply really any rules that you know. So whenever you see composite bases (non-prime bases), there's a very high likelihood that you'll want to break the bases down into prime factors so that you can find common bases.
Here, your bases are 5, 4, 2, and 10. Just by breaking those down to primes, you'll have only 2 and 5 as bases, and you'll have each represented on both sides of the equation. That's an ideal starting point: fewer bases, common bases, and a balanced equation.
With exponent problems in which there are multiple bases, if you're in doubt as to where to start, try breaking the bases down into prime factors and very often you'll see that simplify the problem pretty quickly.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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