To simplify the expression \((7m^{-3}n^8)^{-2}\), follow these steps:

### Step 1: Apply the Power Rule
When you raise a power to another power, multiply the exponents:
\[
(7m^{-3}n^8)^{-2} = 7^{-2} \cdot (m^{-3})^{-2} \cdot (n^8)^{-2}
\]

### Step 2: Simplify Each Term
Now, simplify each part:
- \(7^{-2} = \frac{1}{7^2} = \frac{1}{49}\)
- \((m^{-3})^{-2} = m^{(-3) \cdot (-2)} = m^6\)
- \((n^8)^{-2} = n^{8 \cdot (-2)} = n^{-16}\)

So, the expression simplifies to:
\[
\frac{m^6}{49n^{16}}
\]

This is the simplified form of the given expression.

Would you like more details or have any questions?

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Here are some related questions you might find helpful:
1. How do you simplify an expression with negative exponents?
2. What is the power rule in exponents?
3. How do you deal with coefficients when raising them to a power?
4. Can you explain how to simplify an expression with multiple variables and exponents?
5. What are the common mistakes to avoid when working with exponents?

**Tip:** When simplifying expressions with negative exponents, remember that they can be converted to positive exponents by taking the reciprocal.

Learn how to simplify the expression (7m^-3n^8)^-2 using the power rule and exponent rules. Follow a step-by-step solution to convert negative exponents to positive and simplify terms effectively. Suitable for students in Grades 9-12.

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