Forward Difference of Power

Theorem

 * $\Delta c^{x} = (c-1)c^{x}$

where $\Delta$ represents the forward difference.

Corollary

 * $\Delta 2^{x} = 2^{x}$

Proof
From the definitions:

Proof of Corollary

 * $\Delta 2^{x} = (2-1)2^{x} = 2^{x}$