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.