Question : Which value among $3^{200},2^{300},$ and $7^{100}$ is the largest?
Option 1: $3^{200}$
Option 2: $2^{300}$
Option 3: $7^{100}$
Option 4: All are equal.
Correct Answer: $3^{200}$
Solution : Given: $3^{200},2^{300},$ and $7^{100}$ $3^{200}=(3^{2})^{100}=9^{100}$ $2^{300}=(2^{3})^{100}=8^{100}$ $7^{100}=(7^{1})^{100}=7^{100}$ Thus, the largest number is $3^{200}$. Hence, the correct answer is $3^{200}$.
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