Divide the following and express your answer in appropriate scientific notation: \[ \left(4.14 \times 10^{53}\right) \div\left(4.5 \times 10^{8}\right) \] quotient \( =\square \)

To divide the numbers, we divide the coefficients and subtract the exponents of ten: 1. Divide the coefficients: \( \frac{4.14}{4.5} \approx 0.92 \). 2. Subtract the exponents: \( 53 - 8 = 45 \). Now we can express \( 0.92 \) in scientific notation, which is \( 9.2 \times 10^{-1} \). So, multiplying this by \( 10^{45} \): \[ (9.2 \times 10^{-1}) \times (10^{45}) = 9.2 \times 10^{44} \] Therefore, the final answer is quotient \( = 9.2 \times 10^{44} \).