Let's solve the problems from the image:

1. $4^2$: $4^2 = 4 \times 4 = 16$ Answer: $16$

2. $2^3$: $2^3 = 2 \times 2 \times 2 = 8$ Answer: $8$

3. $(-4)^3$: $(-4)^3 = (-4) \times (-4) \times (-4) = -64$ Answer: $-64$

4. $(-5)^3$: $(-5)^3 = (-5) \times (-5) \times (-5) = -125$ Answer: $-125$

5. $-2^3$: $-2^3 = -(2 \times 2 \times 2) = -8$ Answer: $-8$

Would you like any additional details or have any questions? Here are some related questions:

1. What is the difference between $(-4)^3$ and $-4^3$?
2. How do you calculate $(-3)^2$ and $-3^2$?
3. What is the result of $3^4$?
4. How do negative bases affect exponents?
5. What is the value of $(-2)^4$?

Tip: When calculating powers with negative bases, be careful with parentheses. For example, $(-4)^3$ is different from $-4^3$.