Calculate. \[ \left(3.0 \times 10^{11}\right)^{4} \] Write your answer in scientific notation.

To calculate \(\left(3.0 \times 10^{11}\right)^{4}\), we can use the property of exponents that states \((a \times b)^{n} = a^{n} \times b^{n}\). Therefore: \[ \left(3.0 \times 10^{11}\right)^{4} = (3.0)^{4} \times (10^{11})^{4} \] Calculating \((3.0)^{4}\): \[ (3.0)^{4} = 3.0 \times 3.0 \times 3.0 \times 3.0 = 81.0 \] Now calculating \((10^{11})^{4}\): \[ (10^{11})^{4} = 10^{11 \times 4} = 10^{44} \] Now we combine the two results: \[ 81.0 \times 10^{44} \] To express this in proper scientific notation, we need the coefficient to be between 1 and 10. We can rewrite \(81.0\) as \(8.1 \times 10^{1}\): \[ 81.0 \times 10^{44} = 8.1 \times 10^{1} \times 10^{44} = 8.1 \times 10^{45} \] Thus, the final answer is: \[ \boxed{8.1 \times 10^{45}} \]