Calculate. \[ \left(5.00 \times 10^{7}\right)^{3} \] Write your answer in scientific notation.

To calculate \(\left(5.00 \times 10^{7}\right)^{3}\), you can utilize the properties of exponents. First, raise the coefficient to the power of 3: \[ (5.00)^{3} = 125.000 \] Next, apply the exponent to the power of ten: \[ (10^{7})^{3} = 10^{21} \] Now, combine these results: \[ 125.000 \times 10^{21} \] To express this in proper scientific notation, you need to represent it as \(1.25 \times 10^{23}\) by moving the decimal point in the coefficient one place to the left and increasing the exponent by 1. Thus, the answer in scientific notation is: \[ \boxed{1.25 \times 10^{23}} \]