We need to simplify the given expression:

$4b^{-3} \cdot 2b^2 \cdot b^{-1}$

Step-by-step solution:

1. Group the constants: Multiply the constants $4$ and $2$: $4 \cdot 2 = 8$

2. Combine the powers of $b$: When multiplying terms with the same base, add their exponents: $b^{-3} \cdot b^2 \cdot b^{-1} = b^{-3 + 2 - 1} = b^{-2}$

3. Final result: So, the simplified expression is: $8b^{-2}$

This can also be written as: $\frac{8}{b^2}$

Would you like more details or have any questions?

Related Questions:

1. How do you simplify more complex expressions with negative exponents?
2. What are the rules for multiplying exponents with the same base?
3. Can you explain how to divide expressions with exponents?
4. How do fractional exponents work in these kinds of expressions?
5. How do you simplify expressions with both negative and fractional exponents?

Tip: When multiplying powers with the same base, always add the exponents.