## Task 3 - 180913

In a circle of young mathematicians, the participants are trying to solve the following problem:

The number 30 is to be represented using exactly one single-digit number exactly nine times, with the symbols of the basic arithmetic operations and parentheses being allowed, and the power notation being permissible.

Show that this is possible for each of the single-digit numbers $1 ; 2 ; 3 ; 4, 5 ; 6 ; 7 ; 8$ and 9! (It suffices to provide an example for each.)


$$
\begin{aligned}
& 30=(1+1)^{1+1+1+1+1}-1-1 \\
& 30=3^{3}+3+3-3+3-3+3-3 \\
& 30=5 \cdot 5+5+5-5+5-5+5-5
\end{aligned}
$$

$$
\begin{aligned}
& 30=(2+2+2)^{2}-2-2-2+2-2 \\
& 30=4 \cdot 4\left(\frac{4+4}{4}\right)-\frac{4}{4}-\frac{4}{4} \\
& 30=6 \cdot 6-6+6-6+6-6+6-6
\end{aligned}
$$

$$
\begin{array}{ll}
30=7+7+7+7+\frac{7+7}{7}+7-7 & 30=8+8+8+8-\frac{8+8}{8}+8-8 \\
30 & =9+9+9+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}
\end{array}
$$