Divide the following and express your answer in appropriate scientific notation: \[ \frac{8.64 \times 10^{-25}}{2.7 \times 10^{13}} \]

To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents. First, divide the coefficients: \[ \frac{8.64}{2.7} \approx 3.2 \] Next, subtract the exponents: \[ -25 - 13 = -38 \] Putting it all together, we get: \[ 3.2 \times 10^{-38} \] Since the coefficient should be between 1 and 10, we rewrite \(3.2\) as \(0.32 \times 10^1\). Therefore, we have: \[ 0.32 \times 10^1 \times 10^{-38} = 0.32 \times 10^{-37} \] For proper scientific notation, we further express \(0.32\) as \(3.2 \times 10^{-1}\), leading to: \[ 3.2 \times 10^{-38 - 1} = 3.2 \times 10^{-39} \] So, the final answer is: \[ 3.2 \times 10^{-39} \]