Simplify and give the answer in exponential form: $(5^{24} \div 5^{6}) \times 5^{2}$

5^{8}

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5^{15}

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5^{20}

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5^{9}

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Solution

The correct option is C $5^{20}$
$(5^{24} \div 5^{6}) \times 5^{2}$

= $(5^{24 - 6}) \times 5^{2}$
[by, applying $(a^{m} \div a^{n}) = a^{m - n}$ ]

= $(5^{18}) \times 5^{2}$

= $(5^{18 + 2})$
[by, applying $(a^{m} \times a^{n}) = a^{m + n}$ ]

= $5^{20}$

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