Let's evaluate each expression:

1. $(-5)^3$

To evaluate $(-5)^3$, we multiply $-5$ by itself three times:

$(-5) \times (-5) \times (-5) = -125$

So, $(-5)^3 = -125$.

2. $(-7)^2$

To evaluate $(-7)^2$, we multiply $-7$ by itself:

$(-7) \times (-7) = 49$

Thus, $(-7)^2 = 49$.

Final Answers

1. $(-5)^3 = -125$
2. $(-7)^2 = 49$

Would you like more details on any part of the solution?

Here are some additional questions related to this problem:

1. How do exponents affect the sign of a number?
2. What would happen if we evaluated $(-5)^2$ instead?
3. Can you explain why $(-7)^3$ would yield a negative answer?
4. How does raising a positive number to an odd power differ from raising a negative number to an odd power?
5. What is the result of $(-2)^4$?

Tip: Remember, when a negative number is raised to an even power, the result is positive. When it’s raised to an odd power, the result is negative.