(-8)to the power of 2     -8to the power of2   8-to the power of2

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!

(-8) to the power of 2, -8 to the power of 2, 8 to the power of -2

Understand how to evaluate expressions with exponents like (-8)^2, -8^2, and 8^-2. Learn the rules for exponents with negative bases and negative exponents with examples and explanations, suitable for students in Grades 8-10.

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