Search code examples
mathalgebra

Expand 2^(k + 1)

http://doyourmath.com/web-algebrator/#c=expand_algexpand&v5=2%5E(k%2B1)

Anyone can explain why does expand 2^(k + 1) equal to (2^k) + 1?

Solution

  • That's not actually possible. 2^(k+1) is always going to be an even number. 2^k + 1 is always going to be an odd number.

    I think you mean 

    2^(k+1) = 2^k * 2^1 = 2^k * 2.

    One way of looking at it is the associative property of multiplication: 

    (2 X 3) X 4 = 2 X (3 X 4)

    No matter how you group the numbers, the outcome will always be equal. In this case we're dealing with exponents, which is a shorthand notation for multiplying a number by itself.