Let's go through the exercises in the image one by one:

1. (α) $\frac{5}{5} = ?$: $\frac{5}{5} = 1$

2. (β) $3 \cdot 3 \cdot 6 \cdot 5 \cdot 6 = ?$: $3 \cdot 3 = 9,\quad 9 \cdot 6 = 54,\quad 54 \cdot 5 = 270,\quad 270 \cdot 6 = 1620$ So the result is: $1620$

3. (γ) $β \cdot β \cdot β \cdot β \cdot β = ?$: Here, assuming $β$ represents a number or variable that is not provided, you would multiply $β$ five times. The result would be: $β^5$

4. (δ) $6 + 6 + \dots + 6$ (32 times): This is equivalent to: $32 \cdot 6 = 192$

5. (ε) $2011 \cdot 2011 \cdot 2011 \cdot 2011 \cdot 2011 = ?$: This would be: $2011^5$ Without full expansion, this remains as $2011$ raised to the power of 5.

Let me know if you would like more details on any of these solutions or need further assistance!

Here are some related questions:

1. What is the value of $3 \cdot 3 \cdot 3 \cdot 6 \cdot 6$?
2. What does it mean when we write $\frac{a}{a}$ for any $a \neq 0$?
3. How do you calculate the power of a variable, like $β^5$?
4. How can you quickly calculate the sum of repeated additions like in problem (δ)?
5. What is $2011^3$?

Tip: When dealing with large powers, you can simplify calculations by using properties of exponents or logarithms.