Simplify and express each of the following in exponential form: ${(2^{3} \times 2)}^{2}$

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Solution

Use appropriate laws of exponents
Given: ${(2^{3} \times 2)}^{2}$
${(2^{3} \times 2)}^{2}$
$= {(2^{3 + 1})}^{2} [∵ a^{m} \times a^{n} = a^{m + n}]$
$= {(2^{4})}^{2}$
${(2^{4})}^{2}$ can be written as ${(2)}^{4 \times 2} = 2^{8}$ $[∵ {(a^{m})}^{n} = a^{m n}]$
${∴ (2^{3} \times 2)}^{2} = 2^{8}$

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