+0  
 
+1
1337
1
avatar+885 

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?

 Sep 3, 2018
 #1
avatar+399 
+1

\(400 = 20^2\), 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

 Sep 3, 2018

3 Online Users

avatar