Simplify and express each of the following in exponential form :
(v) $[{(2^{2})}^{3} \times 3^{6}] \times 5^{6}$

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Solution

Simplifying and expressing in exponential form :
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = [2^{2 \times 3} \times 3^{6}] \times 5^{6}$
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = [2^{6} \times 3^{6}] \times 5^{6}$
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = {(2 \times 3)}^{6} \times 5^{6}$
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = 6^{6} \times 5^{6}$
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = {(6 \times 5)}^{6}$
$[{(2^{2})}^{3} \times 3^{6}] \times 5^{6} = {(30)}^{6}$
Hence, the simplified exponential form of $[{(2^{2})}^{3} \times 3^{6}] \times 5^{6}$ is ${(30)}^{6}$ .

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