Let's evaluate each expression individually:

1. $(-8)^2$

$(-8)^2 = (-8) \times (-8) = 64$

2. $-8^2$

In this expression, the exponent applies only to the 8, not the negative sign: $-8^2 = -(8 \times 8) = -64$

3. $8^{-2}$

In this case, $8$ is raised to the power of $-2$, which gives the reciprocal of $8^2$: $8^{-2} = \frac{1}{8^2} = \frac{1}{64}$

Summary of Results:

1. $(-8)^2 = 64$
2. $-8^2 = -64$
3. $8^{-2} = \frac{1}{64}$

Would you like further details on how exponents interact with negative bases or other questions on this topic?

Here are some related questions to deepen your understanding:

1. What is the difference between $(-x)^n$ and $-x^n$ when $n$ is an even number?
2. How would the result change if we evaluated $(-8)^3$ instead of $(-8)^2$?
3. What happens when a negative base is raised to a fractional power?
4. How does the result of $8^{-2}$ change if the base is replaced with a negative number, like $(-8)^{-2}$?
5. What is the value of $(8)^{0.5}$ and how does it relate to square roots?

Tip: Remember that parentheses around negative bases are essential when raising them to a power, especially if using a calculator or certain programming languages!