Calculate \[ \left(2.0 \times 10^{9}\right)^{-2} \] Write your answer in scientific notation.

To calculate \(\left(2.0 \times 10^{9}\right)^{-2}\), we first handle the coefficient and the exponent separately. 1. For the coefficient \(2.0^{-2}\): \[ 2.0^{-2} = \frac{1}{(2.0)^2} = \frac{1}{4.0} = 0.25 \] 2. For the exponent \(10^{9}\): \[ (10^{9})^{-2} = 10^{-18} \] Now, we combine these results: \[ \left(2.0 \times 10^{9}\right)^{-2} = 0.25 \times 10^{-18} \] To express \(0.25\) in scientific notation, we rewrite it as \(2.5 \times 10^{-1}\). Therefore, we have: \[ 2.5 \times 10^{-1} \times 10^{-18} = 2.5 \times 10^{-1 - 18} = 2.5 \times 10^{-19} \] The final answer in scientific notation is: \[ \boxed{2.5 \times 10^{-19}} \]