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Simplify the following. No parentheses and no negative exponents in your answer

To simplify the expression \( \left( -2p^9 \right)^{-3} \) without parentheses and without negative exponents, follow these steps:

1. Apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\).
   In this case:
   \[
   \left( -2p^9 \right)^{-3} = (-2)^{-3} \cdot (p^9)^{-3}
   \]
2. Simplify each part:
   \[
   (-2)^{-3} = -\frac{1}{8}, \quad (p^9)^{-3} = p^{-27}
   \]

3. Combine the terms:
   \[
   -\frac{1}{8} \cdot p^{-27} = -\frac{1}{8p^{27}}
   \]

So, the simplified expression is:
\[
-\frac{1}{8p^{27}}
\]

Would you like further details or have any questions?

Here are 5 related questions you might explore:
1. What is the power of a product rule, and how does it apply here?
2. How do you handle negative exponents in general?
3. What happens if you simplify an expression like \((3x^5)^4\)?
4. Can you simplify \( (2a^2b^3)^4 \) and describe each step?
5. How does simplifying fractions with exponents differ from regular fraction simplification?

**Tip**: When dealing with negative exponents, remember that they can always be rewritten as reciprocals (e.g., \(x^{-n} = \frac{1}{x^n}\)).

Simplify the following expression: (-2p^9)^-3. No parentheses and no negative exponents in your answer.

Learn how to simplify the expression (-2p^9)^-3 by applying exponent rules, including the power of a power rule and the negative exponent rule. This solution involves simplifying to -1/(8p^27), making it suitable for students in Grades 9-11.

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