Final answer:
To simplify the expression (2uv³) / (w^(-1)⁻² (v⁻³ w⁷)), you need to use the laws of exponents. First, simplify the denominator. Then, multiply the terms together and combine like terms.
Step-by-step explanation:
To simplify the expression (2uv³) / (w^(-1)⁻² (v⁻³ w⁷), we need to use the laws of exponents. First, let's simplify the denominator using the rule that says w^(-a) = 1 / w^a. So, w^(-1)⁻² becomes 1 / w^(1)². Now we can simplify the expression:
(2uv³) / (1 / w^(1)² (v⁻³ w⁷))
To divide by a fraction, we can multiply by the reciprocal. So, we can rewrite the expression as:
(2uv³) * (w^(1)² (v⁻³ w⁷)) / 1
Now multiplying the terms together, we get:
2u w^(1)² v³ v⁻³ w⁷
Simplifying further, we can combine the like terms:
2u w^(1+2) v^(3-3) w⁷
Therefore, the simplified expression is 2u w³ w⁷ which can be written as 2u w^(3+7), or 2u w^10.