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.