Let's break down the expression step by step:

$(m^{-3})(2m^{-3}n^4)(4m)$

1. First, simplify the powers of $m$:

   $(m^{-3})(m^{-3})(m)$

   When multiplying terms with the same base, you add the exponents:

   $m^{-3} \times m^{-3} \times m = m^{-3 + (-3) + 1} = m^{-5}$

2. Now, simplify the rest of the terms:

   $(2n^4)(4)$

   Multiply the constants:

   $2 \times 4 = 8$

   So the expression becomes:

   $8n^4 m^{-5}$

The simplified result is:

$8m^{-5}n^4$

Final Answer:

$8m^{-5}n^4$

Would you like to go over more details or have any further questions?

Here are 5 related questions to explore:

1. How do you handle expressions with negative exponents?
2. What happens if you have fractions with exponents in them?
3. How do you simplify expressions with multiple variables and exponents?
4. What are the rules for multiplying terms with different variables?
5. Can you explain how to simplify powers of negative numbers?

Tip: Remember that when multiplying terms with the same base, you always add the exponents.