Which value among 3^{200}, 2^{300} and 7^{100 | vedclass

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Question

(A) To compare the values $3^{200}, 2^{300}$,and $7^{100}$,we can simplify the exponents by finding the greatest common divisor of the exponents,which

Vedclass · Accepted Answer

$3^{200}$

Vedclass · Answer

(A) To compare the values $3^{200}, 2^{300}$,and $7^{100}$,we can simplify the exponents by finding the greatest common divisor of the exponents,which is $100$.$1$. Rewrite each expression as a power of $100$:$3^{200} = (3^2)^{100} = 9^{100}$$2^{300} = (2^3)^{100} = 8^{100}$$7^{100} = 7^{100}$$2$. Now,compare the bases since the exponents are the same $(100)$:$9^{100}, 8^{100}, 7^{100}$$3$. Since $9 > 8 > 7$,it follows that $9^{100} > 8^{100} > 7^{100}$.Therefore,$3^{200}$ is the largest value.

Which value among $3^{200}, 2^{300}$ and $7^{100}$ is the largest?

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