Showing that a $3^n$ digit number whose digits are all equal is divisible by $3^n$ 
Let $c$ be a $3^n$ digit number whose digits are all equal. Show that $3^n$ divides
  $c$.

I have no idea how to solve these types of problems. Can anybody help me please?

Because the digits sum to a multiple of $3$, a block of $3$ identical digits is divisible by $3$.
$3$ of those blocks of $3$ digits, having been divided by $3$, is also divisible by $3$.
$3$ of those blocks of $3^2$ digits, having been divided by $3^2$, is also divisible by $3$.
$3$ of those blocks of $3^3$ digits, having been divided by $3^3$, is also divisible by $3$.
and so on. For example,
$\begin{align}
&111/3\\
=&037
\end{align}$
$\begin{align}
&111\ 111\ 111/3^2\\
=&037\ 037\ 037/3\\
=&012\ 345\ 679
\end{align}$
$\begin{align}
&111111111\ 111111111\ 111111111/3^3\\
=&037037037\ 037037037\ 037037037/3^2\\
=&012345679\ 012345679\ 012345679/3\\
=&004115226\ 337448559\ 670781893
\end{align}$
