Divide. \[ \frac{4 \times 10^{8}}{8 \times 10^{-5}} \]

To solve the division, we can simplify the expression: \[ \frac{4 \times 10^{8}}{8 \times 10^{-5}} = \frac{4}{8} \times \frac{10^{8}}{10^{-5}} \] First, simplify \( \frac{4}{8} \): \[ \frac{4}{8} = \frac{1}{2} \] Next, simplify \( \frac{10^{8}}{10^{-5}} \) using the properties of exponents: \[ \frac{10^{8}}{10^{-5}} = 10^{8 - (-5)} = 10^{8 + 5} = 10^{13} \] Now, multiply the simplified terms together: \[ \frac{1}{2} \times 10^{13} = \frac{10^{13}}{2} \] Calculating \( \frac{10^{13}}{2} \): \[ 10^{13} = 10000000000000 \] So, \[ \frac{10000000000000}{2} = 5000000000000 \] Thus, the final result is: \[ 5 \times 10^{12} \]