Well, let's see.
When you need to multiply two numbers that are both powers of the same
base, that's the same as just adding the exponents. So for this problem,
you could use that idea backwards.
2^9 could be the product of (2^4) times (2^5) .
-- Multiply 2 together 4 times. (16)
-- Multiply 2 together 5 times. (32)
-- Then multiply those two numbers. (16 x 32 = 512)
-- 512 is 2^9 and you didn't have to multiply nine 2s together.
(Maybe you saved yourself some effort, but you didn't save ME any.)