I saw a problem recently that looked like this:
Assume $w$ and $z$ are positive. If $z^{4w} = 64$, what does $z^{6w}$ equal?
And I had absolutely no idea how to even begin attempting this equation. How could I have gone about figuring out the answer? This question was multiple choice, though I don't remember the answers available to me.
Given $z^{4w} = 64, z^{6w} =$ ?
We need to find a relationship between the exponents. Since $x^{ab} = (x^{a})^b$,
$$\Large{z^{6w} = z^{4w\cdot1.5}} = (z^{4w})^{1.5} = 64^{1.5} = 512$$