Question : The quotient when $10^{100}$ is divided by $5^{75}$ is:
Option 1: $2^{25}×10^{75}$
Option 2: $10^{25}$
Option 3: $2^{75}$
Option 4: $2^{75}×10^{25}$
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Correct Answer: $2^{75}×10^{25}$
Solution : Given: $10^{100}$ is divided by $5^{75}$. = $\frac{10^{100}}{5^{75}}$ = $\frac{(2×5)^{100}}{5^{75}}$ = $\frac{2^{100}×5^{100}}{5^{75}}$ = $2^{100}×\frac{5^{100}}{5^{75}}$ By using, $\frac{a^{m}}{a^{n}}=a^{(m–n)}$ = $2^{100}×5^{(100-75)}$ = $2^{100}×5^{25}$ = $2^{75}×2^{25}×5^{25}$ = $2^{75}×10^{25}$ Hence, the correct answer is $2^{75}×10^{25}$.
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