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To express 20 as a sum of different powers of 2, we would write \(20 = 2^4 + 2^2\). 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?

ant101  Sep 3, 2018
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\(400 = 20^2\), so we have \((2^4 + 2^2)^2 = (2^4)^2 + 2(2^4)(2^2)+(2^2)^2 = 2^8 + 2^7 + 2^4\)\(8+7+4=19\).

 

- Daisy

dierdurst  Sep 3, 2018

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