Diane needs to keep these numbers in scientific notation. How could she find the product of these numbers? \( \left(4.8 \times 10^{6}\right) \times\left(3.2 \times 10^{9}\right) \)

To find the product of \( \left(4.8 \times 10^{6}\right) \times \left(3.2 \times 10^{9}\right) \) while keeping the result in scientific notation, follow these steps: 1. **Multiply the Coefficients:** \[ 4.8 \times 3.2 = 15.36 \] 2. **Add the Exponents:** When multiplying numbers in scientific notation with the same base (which is 10 in this case), you add the exponents. \[ 10^{6} \times 10^{9} = 10^{6+9} = 10^{15} \] 3. **Combine the Results:** \[ 15.36 \times 10^{15} \] 4. **Adjust to Standard Scientific Notation:** Scientific notation requires that the coefficient is between 1 and 10. To adjust \( 15.36 \times 10^{15} \) accordingly: \[ 15.36 \times 10^{15} = 1.536 \times 10^{1} \times 10^{15} = 1.536 \times 10^{16} \] This ensures the coefficient \(1.536\) is within the required range for scientific notation. **Final Answer:** \[ 1.536 \times 10^{16} \]