Question 50

Determine the greatest number among the following four numbers

Solution

$$2^{300}=\left(2^3\right)^{100}=8^{100}$$

$$3^{200}=\left(3^2\right)^{100}=9^{100}$$

$$2^{100}+3^{100}<6^{100}$$ (Because if $$a+b<c$$, then $$a^x+b^x, given a,b,c, and x are greater than 1)

$$4^{100}$$

Thus, among all these, $$9^{100}$$ is highest and thus, $$3^{200}$$ is the greatest value.

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