Question

Find the largest number $2^{300},3^{200}$.

Answer 1

Given, $2^{300},3^{200}$.

Now, $2^{300}=(2^3{)}^{100}=8^{100}$.....(1).

Again, $3^{200}=(3^2{)}^{100}=9^{100}$.....(2).

Since $9>8$, then we get,

$9^{100}>8^{100}$

or, $3^{200}>2^{300}$.

So $3^{200}$ is the largest.