To find the total storage of the mobile phone after purchasing the additional space, we need to add the current storage and the additional storage together in scientific notation.
- Current storage: \( 1.28 \times 10^{11} \) bytes
- Additional storage: \( 384,000,000,000 \) bytes
First, we convert the additional storage to scientific notation: \[ 384,000,000,000 = 3.84 \times 10^{11} \text{ bytes} \]
Now, we add the two amounts together: \[ 1.28 \times 10^{11} + 3.84 \times 10^{11} \]
Adding these together: \[ (1.28 + 3.84) \times 10^{11} = 5.12 \times 10^{11} \text{ bytes} \]
Thus, the total storage of the phone, after purchasing the additional bytes, would be: \[ \boxed{5.12 \times 10^{11}} \text{ bytes} \]