11.48 Which is greater: $3^{400}$ or $4^{300} ?$
11.48 Let's bring the given numbers to the same exponent, equal to 100. We have

$$
3^{400}=3^{4 \cdot 100}=\left(3^{4}\right)^{100} ; 4^{300}=4^{3 \cdot 100}=\left(4^{3}\right)^{100}
$$

Since of the two powers with the same positive exponent 100, the one with the larger base is greater, then $3^{400}>4^{300}$.