# Thread: Subtracting exponents with the same base

1. ## Subtracting exponents with the same base

Hey everyone,

A small queston

2^(k+1) - 2^k

How did they get 2^k (2-1)??

thank you

2. Originally Posted by Thetheorycase
Hey everyone,

A small queston

2^(k+1) - 2^k

How did they get 2^k (2-1)??

thank you
A common factor is $2^{k}$ since $2^{k+1} = 2^k \cdot 2^1 = 2^k \cdot 2$ using the well known index law.

Therefore: $2^{k+1} - 2^k = 2^k (2 - 1)$.

3. observe that
$2^{k+1}=2\times 2^k$.
now can you continue from here?