Precalculus (6th Edition) Blitzer

The product rule for exponents is when multiplying two powers with the same base, keep the same base and add the exponents ($x^{y} \times x^{z} = x^{y+z}$).
To solve $2^{3} \times 2^{5}$, add the 3 and the 5 in the exponents and keep base as 2 to get $2^{8}$. This is equal to 256.