down the result in scientific notation. \( \frac{\left(9.6 \times 10^{-6}\right) \times\left(7.5 \times 10^{-10}\right)}{\left(2.4 \times 10^{-5}\right)^{2}} \)

To solve the expression \( \frac{\left(9.6 \times 10^{-6}\right) \times\left(7.5 \times 10^{-10}\right)}{\left(2.4 \times 10^{-5}\right)^{2}} \), let's break it down step by step. 1. **Calculate the numerator:** \[ (9.6 \times 10^{-6}) \times (7.5 \times 10^{-10}) = 9.6 \times 7.5 \times 10^{-6} \times 10^{-10} = 72.0 \times 10^{-16} \] We can express \( 72.0 \) in scientific notation: \[ 72.0 = 7.2 \times 10^{1} \] Thus: \[ 9.6 \times 10^{-6} \times 7.5 \times 10^{-10} = 7.2 \times 10^{1} \times 10^{-16} = 7.2 \times 10^{-15} \] 2. **Calculate the denominator:** \[ (2.4 \times 10^{-5})^2 = 2.4^2 \times (10^{-5})^2 = 5.76 \times 10^{-10} \] Here, \( 5.76 \) can be expressed in scientific notation as: \[ 5.76 = 5.76 \times 10^{0} \] So, the denominator becomes: \[ 5.76 \times 10^{-10} \] 3. **Now, combine the results:** \[ \frac{7.2 \times 10^{-15}}{5.76 \times 10^{-10}} = \frac{7.2}{5.76} \times 10^{-15 - (-10)} = \frac{7.2}{5.76} \times 10^{-15 + 10} = \frac{7.2}{5.76} \times 10^{-5} \] 4. **Calculate \( \frac{7.2}{5.76} \):** \[ \frac{7.2}{5.76} = 1.25 \] 5. **Combine it all:** \[ 1.25 \times 10^{-5} \] Thus, the final result in scientific notation is: \[ \boxed{1.25 \times 10^{-5}} \]