SOLUTION: To express 20 as a sum of different powers of 2, we would write 20 = 24 + 22. The sum of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two

Question 203189: To express 20 as a sum of different powers of 2, we would write 20 = 24 + 22. The sum of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of
the exponents of these powers?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

We will use the above and the fact that

to solve this problem.

Substituting the right side of the first equation in for the 20 in the second equation:

You can use FOIL to multiply the right side. Or you can use the the factoring pattern: with "a" = and "b" = . Either way we get:

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