See graph and explanations.
Work Step by Step
Step 1. Graph the function $y=2^x$; as the inequality does not include an equal sign, make the boundary dashed. Step 2. Using a test point away from the boundary, such as $(0,0)$, we have $0\gt2^0=1$ which is not true; thus the other side without this test point should be shaded as shown in the figure.