To find the total storage after buying the additional bytes, we need to add:
- The original storage: \(1.28 \times 10^{11}\) bytes
- The additional storage: \(384,000,000,000\) bytes
First, let's express the additional storage in scientific notation:
\[ 384,000,000,000 = 3.84 \times 10^{11} \]
Now, we can add the two quantities:
\[ 1.28 \times 10^{11} + 3.84 \times 10^{11} = (1.28 + 3.84) \times 10^{11} = 5.12 \times 10^{11} \]
Therefore, the total storage of the phone after purchasing the additional bytes is:
\[ \boxed{5.12 \times 10^{11}} \]