20) How many digits does the number (123456789) ${ }^{6}$ have?

![](https://cdn.mathpix.com/cropped/2024_04_17_c3d7afe478310a3de07bg-2.jpg?height=265&width=231&top_left_y=449&top_left_x=2521)
(A) 16
(B) 48
(C) 49
(D) 50
(E) 54 .
20) The answer is $(\mathbf{C})$.

We have $(123456789)^{6}=\left(\alpha \cdot 10^{8}\right)^{6}=\alpha^{6} \cdot 10^{48}$, where $\alpha=1.23 \ldots$; thus $\alpha^{2}<2, \alpha^{6}<8$; therefore the number of digits is the same as $10^{48}$, which is 49.