To find the total storage after buying the additional bytes, you would add the two amounts of storage together:
- Current storage: \(1.28 \times 10^{11}\) bytes
- Additional storage: \(384,000,000,000\) bytes
First, convert \(384,000,000,000\) bytes into scientific notation:
\[ 384,000,000,000 = 3.84 \times 10^{11} \]
Now add the two amounts:
\[ 1.28 \times 10^{11} + 3.84 \times 10^{11} = (1.28 + 3.84) \times 10^{11} = 5.12 \times 10^{11} \]
Thus, the total storage of the phone after purchasing the additional bytes is:
\[ \boxed{5.12 \times 10^{11}} \]