Simplify : $2^{30} + 2^{30} + 2^{30} + 2^{30}$

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Solution

Given $2^{30} + 2^{30} + 2^{30} + 2^{30}$
$\begin{matrix} 2^{30} + 2^{30} + 2^{30} + 2^{30} = 4 \times 2^{30} \\ = 2^{2} \times 2^{30} [∵ a^{m} \times a^{n} = a^{(m + n)}] \\ = 2^{32} \end{matrix}$
Hence the simplified form of $2^{30} + 2^{30} + 2^{30} + 2^{30}$ is $2^{32}$ .

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