From Förberedande kurs i matematik 1

Because the base is the same in both factors, the exponents can be combined according to the power rules

\displaystyle 2^{9}\centerdot 2^{-7}=2^{9-7}=2^{2}=4

Alternatively, the expressions for the powers can be expanded completely and then cancelled out,

\displaystyle \begin{align} & 2^{9-7}=2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot \frac{1}{2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2\centerdot 2} \\ & \\ & =2\centerdot 2=4 \\ \end{align}