I'm not a huge fan of any kind of memorization. However, if you can memorize a few important powers, then you'll be able to identify useful problem-solving approaches if you recognize certain powers.
Consider an example where we must solve an equation for x: 27^x = 81^(x-1)
If we're able to recognize that we can rewrite both 27 and 81 as powers of 3, then we're well on our way to solving the equation.
However, without having memorized 3^3 = 27 and 3^4 = 81, you may have difficulty answering the question (even if your addition/multiplication skills are excellent)
Cheers,
Brent
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