Simplifying powers with the same base

Statement

Simplify and compute: $\frac{2^{10}\cdot 2^{3}}{2^{5}}.$

Solution

By the laws of exponents, add the exponents in the numerator and subtract the one in the denominator: $\frac{2^{10}\cdot 2^{3}}{2^{5}} = 2^{10+3-5} = 2^{8} = \boxed{256}.$