Simplify and express each of the following in exponential form :
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7}$

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Solution

Simplifying and expressing in exponential form :
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = [5^{2 \times 3} \times 5^{4}] \div 5^{7}$
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = [5^{6} \times 5^{4}] \div 5^{7}$
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = [5^{6 + 4}] \div 5^{7}$
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = 5^{10} \div 5^{7}$
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = 5^{10 - 7}$
$[{(5^{2})}^{3} \times 5^{4}] \div 5^{7} = 5^{3}$
Hence, the simplified exponential form of $[{(5^{2})}^{3} \times 5^{4}] \div 5^{7}$ is $5^{3}$ .

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