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

Algebra ->  Exponents -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
20+=+2%5E4+%2B+2%5E2
We will use the above and the fact that
400+=+20%5E2
to solve this problem.

Substituting the right side of the first equation in for the 20 in the second equation:
400+=+%282%5E4+%2B+2%5E2%29%5E2
You can use FOIL to multiply the right side. Or you can use the the factoring pattern: %28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2B+b%5E2 with "a" = 2%5E4 and "b" = 2%5E2. Either way we get: