a) \( \left(3.9 \times 10^{9}\right)+\left(6.4 \times 10^{7}\right) \) b) \( \left(8.4 \times 10^{-11}\right)-\left(5.1 \times 10^{-12}\right) \) Give your answers in standard form.

To solve the problems, we need to ensure that the numbers are expressed in the same power of ten before performing the operations. ### a) \( \left(3.9 \times 10^{9}\right)+\left(6.4 \times 10^{7}\right) \) First, we convert \(6.4 \times 10^{7}\) to the same power of ten as \(3.9 \times 10^{9}\): \[ 6.4 \times 10^{7} = 0.064 \times 10^{9} \] Now we can add the two numbers: \[ 3.9 \times 10^{9} + 0.064 \times 10^{9} = (3.9 + 0.064) \times 10^{9} = 3.964 \times 10^{9} \] So, the answer for part a) is: \[ \boxed{3.964 \times 10^{9}} \] ### b) \( \left(8.4 \times 10^{-11}\right)-\left(5.1 \times 10^{-12}\right) \) Next, we convert \(5.1 \times 10^{-12}\) to the same power of ten as \(8.4 \times 10^{-11}\): \[ 5.1 \times 10^{-12} = 0.051 \times 10^{-11} \] Now we can subtract the two numbers: \[ 8.4 \times 10^{-11} - 0.051 \times 10^{-11} = (8.4 - 0.051) \times 10^{-11} = 8.349 \times 10^{-11} \] So, the answer for part b) is: \[ \boxed{8.349 \times 10^{-11}} \]