To find the total storage after purchasing the additional bytes, we need to add the two storage amounts together:
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The initial storage of the mobile phone: \[ 1.28 \times 10^{11} \text{ bytes} \]
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The additional storage that can be purchased: \[ 384,000,000,000 \text{ bytes} = 3.84 \times 10^{11} \text{ bytes} \]
Now, we add these two values together: \[ 1.28 \times 10^{11} + 3.84 \times 10^{11} \] First, we can add them directly since they are already in the same order of magnitude: \[ (1.28 + 3.84) \times 10^{11} = 5.12 \times 10^{11} \text{ bytes} \]
Therefore, the total storage of the phone after buying the additional bytes is: \[ \boxed{5.12 \times 10^{11} \text{ bytes}} \]