$\\frac{2^{4} \\cdot 2^{4}}{2^{3}}$

$\frac{2^{4} \cdot 2^{4}}{2^{3}}$

When multiplying like bases, add exponents: $2^{4} \cdot 2^{4} = 2^{4+4} = 2^{8}$

When dividing like bases, subtract exponents: $\frac{2^{8}}{2^{3}} = 2^{8-3} = 2^{5}$

Compute the power of 2: $2^{5}=32$

32