To simplify the expression \(\frac{m^{-2}n^{16}}{m^4n^2}\), follow these steps:

1. **Combine the bases**: Use the properties of exponents to simplify expressions with the same base. 

2. **Simplify the \(m\) terms**: 
   \[
   \frac{m^{-2}}{m^4} = m^{-2 - 4} = m^{-6}
   \]

3. **Simplify the \(n\) terms**:
   \[
   \frac{n^{16}}{n^2} = n^{16 - 2} = n^{14}
   \]

4. **Combine the simplified terms**:
   \[
   m^{-6}n^{14}
   \]

So, the simplified expression is:

\[
m^{-6}n^{14}
\]

Would you like further details, or do you have any questions?

Here are some related questions for further exploration:

1. How do you simplify expressions with negative exponents?
2. What are the rules for dividing exponents with the same base?
3. How do you simplify an expression with multiple bases and exponents?
4. How do you rewrite an expression with negative exponents using positive exponents?
5. What happens when the bases are different but the exponents are the same?

**Tip:** When simplifying expressions with exponents, remember that dividing powers with the same base means subtracting the exponents.

This guide explains how to simplify the expression m^-2n^16/m^4n^2 by applying the laws of exponents. Follow step-by-step instructions to combine bases, subtract exponents, and reach the final simplified expression m^-6n^14. Ideal for students in Grades 8-10.

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