Memorizing Exponents/Roots

What exponents/roots do you recommend to have memorized? I watched a video where Greg said to memorize the powers of 3 up to 3^5 (3^1, 3^2,…, 3^5), and the same for base 4. My question is, what other bases should I know, and how high of a power should I go up to? For example, the cube root of 343 is 7 (343^(1/3) = 7). Is this something I should have memorized, or should I just solve for it whenever it comes up in the exam?

You don’t need to memorize any of this