. Can you calculate $11^{3}$? $11^{4}$?
We notice that

$$
\begin{aligned}
& 11^{0}=1 \\
& 11^{1}=11 \\
& 11^{2}=121 \\
& 11^{3}=1331 \\
& 11^{4}=14641
\end{aligned}
$$

These are exactly the lines of Pascal's Triangle! To explain this phenomenon, observe that if we try to expand $(10+1)(10+1)(10+1)(10+1)$, then we find

$$
10^{4}+\binom{4}{3} 10^{3}+\binom{4}{2} 10^{2}+\binom{4}{1} 10^{1}+1
$$

Non-essential remark: in fact, we have demonstrated a particular case of the (abstract) binomial theorem.

$$
(x+y)^{n}=x^{n}+\binom{n}{1} \times x^{n-1} \times y+\cdots+\binom{n}{n-1} \times x^{n-1} \times y+y^{n}
$$