$
\begin{array}{l}
\left( {10 + 1} \right)^5 = \\
\sum\limits_{k = 0}^5 {\left( {\begin{array}{*{20}c}
5 \\
k \\
\end{array}} \right)} 10^{5 - k} \cdot 1^k = \\
\left( {\begin{array}{*{20}c}
5 \\
0 \\
\end{array}} \right)10^5 \cdot 1^0 + \left( {\begin{array}{*{20}c}
5 \\
1 \\
\end{array}} \right)10^4 \cdot 1^1 + \left( {\begin{array}{*{20}c}
5 \\
2 \\
\end{array}} \right)10^3 \cdot 1^2 + ... \\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,... + \left( {\begin{array}{*{20}c}
5 \\
3 \\
\end{array}} \right)10^2 \cdot 1^3 + \left( {\begin{array}{*{20}c}
5 \\
4 \\
\end{array}} \right)10^1 \cdot 1^4 + \left( {\begin{array}{*{20}c}
5 \\
5 \\
\end{array}} \right)10^0 \cdot 1^5 = \\
\left( {\begin{array}{*{20}c}
5 \\
0 \\
\end{array}} \right)10^5 + \left( {\begin{array}{*{20}c}
5 \\
1 \\
\end{array}} \right)10^4 + \left( {\begin{array}{*{20}c}
5 \\
2 \\
\end{array}} \right)10^3 + \left( {\begin{array}{*{20}c}
5 \\
3 \\
\end{array}} \right)10^2 + \left( {\begin{array}{*{20}c}
5 \\
4 \\
\end{array}} \right)10^1 + \left( {\begin{array}{*{20}c}
5 \\
5 \\
\end{array}} \right)10^0 = \\
10^5 + 5 \cdot 10^4 + \frac{{5 \cdot 4}}{2}10^3 + \frac{{5 \cdot 4 \cdot 3}}{{2 \cdot 3}}10^2 + 5 \cdot 10^1 + 10^0 = \\
10^5 + 5 \cdot 10^4 + 10 \cdot 10^3 + 10 \cdot 10^2 + 5 \cdot 10^1 + 10^0 = \\
100.000 + 50.000 + 10.000 + 1.000 + 50 + 1 = \\
100.000 + 60.000 + 1.000 + 50 + 1 = \\
161.051 \\
\end{array}
$
Meer moet het niet zijn...
Zie Machten van 11 [http://wiskundeleraar.blogspot.com/2018/11/machten-van-11.html]
WvR
25-11-2018