The expression given is $m^4 \cdot 2m^{-2}$.

To simplify this expression, follow these steps:

1. Combine the powers of $m$ using the property of exponents $a^m \cdot a^n = a^{m+n}$:

$m^4 \cdot 2m^{-2} = 2 \cdot m^{4 + (-2)} = 2m^2$

So, the simplified expression is:

$2m^2$

Would you like more details or have any questions?

Here are some related questions:

1. How do you simplify expressions with negative exponents?
2. Can you explain the rules for multiplying powers of the same base?
3. What happens if you have a zero exponent in an expression?
4. How do you handle expressions with both positive and negative exponents?
5. Can you apply these rules to a more complex expression, such as $m^3 \cdot 4m^{-5}$?
6. What if the base is a fraction, like $\left(\frac{m}{n}\right)^4 \cdot 2\left(\frac{m}{n}\right)^{-2}$?
7. How would you simplify an expression involving division of powers with the same base?
8. What are some common mistakes to avoid when working with exponents?

Tip: Always remember that when multiplying like bases, you add their exponents, and when dividing, you subtract them.