The expression \( a^8 : -a^8 \) represents the division of \( a^8 \) by \( -a^8 \). Let's simplify this:

\[
\frac{a^8}{-a^8} = -1
\]

This is because any non-zero value divided by itself is 1, but with the negative sign in the denominator, the result is \(-1\).

### Final Answer:
\[
\frac{a^8}{-a^8} = -1
\]

Would you like more details or have any questions?

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Here are some related questions to consider:
1. What is the general rule for dividing powers with the same base?
2. How would this change if the powers were different, e.g., \( a^8 : -a^5 \)?
3. How do you handle division with negative exponents?
4. What happens if \( a = 0 \) in this expression?
5. How would you apply this in a real-world scenario involving ratios or proportions?

**Tip:** When dividing powers with the same base, the exponents subtract.

Learn how to simplify the expression a^8 divided by -a^8 using exponent rules. This detailed explanation covers division of powers, negative signs, and properties of exponents. Perfect for students in Grades 8-10.

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