In this problem, I guess b is larger, but not know how to prove it without going to lengthy calculations. It is highly appreciated if anyone can give me a help.
Which number is larger
$$\begin{align}
&\textrm{(a)}\quad 7^{94}
&\quad\textrm{(b)}\quad 9^{91}
\end{align}$$
Best Answer
The first is $7^{91}\times 343$. The second is $7^{91}\times(9/7)^{91}$. Since $\frac{9^3}{7^3}\gt 2$, it follows that $(9/7)^{91}$ is much much bigger than $343$.