Final answer:
To simplify the expression 8m² / (16m⁻³) * (m² - m - 6) / 4m³, you can divide both the numerator and denominator by 4m². Next, multiply the terms with the same bases and simplify the expression by dividing the terms with the same bases.
Step-by-step explanation:
To simplify the expression, we can cancel out the common factors in the numerator and denominator. In this case, we can divide both the numerator and denominator by 4m². This gives us:
(8m² / (16m⁻³)) * (m² - m - 6) / 4m³ = 2m⁴ * (m² - m - 6) / m³
Next, we can simplify the expression further by multiplying the terms with the same bases. This gives us
2m⁴ * (m² - m - 6) / m³ = 2m⁶ - 2m⁵ - 12m⁴ / m³
Finally, we can simplify the expression by dividing the terms with the same bases. This gives us:
2m⁶ - 2m⁵ - 12m⁴ / m³ = 2m³ - 2m² - 12m