1. Among the numbers $3^{8}, 4^{7}, 5^{6}, 6^{5}$, the largest one is ( ).
(A) $3^{8}$
(B) $4^{7}$
(C) $5^{6}$
(D) $6^{5}$
-1. (B)
$\because 4^{7}>3^{8} \Leftrightarrow\left(\frac{4}{3}\right)^{7}>3$, and indeed $\left(\frac{4}{3}\right)^{7}=\left(1+\frac{1}{3}\right)^{7}>1+\frac{7}{3}>3$.
$4^{7}>5^{6} \Leftrightarrow\left(\frac{5}{4}\right)^{6}6^{5} \Leftrightarrow\left(\frac{5}{6}\right)^{6}>\frac{1}{6}$, and $\left(\frac{5}{6}\right)^{3}=\left(\frac{125}{216}\right)^{2}>\left(\frac{1}{2}\right)^{2}=\frac{1}{4}>\frac{1}{6}$. $\therefore 4^{7}>5^{6}>6^{5}$. Among the four numbers, the largest is $4^{7}$. Note: This problem can also be directly determined by the results of the exponentiation operations.