Final answer:
The expression (5a⁴ / -2(a⁴m⁻⁴)⁻¹) simplifies to -5a⁸m⁴ / 2 by applying the rules of negative exponents and multiplication of exponents.
Step-by-step explanation:
To simplify the expression (5a⁴ / -2(a⁴m⁻⁴)⁻¹), we must apply the rules of exponents. Negative exponents flip the base to the other part of the fraction; therefore, we move (a⁴m⁻⁴) to the numerator. So, we get:
- 5a⁴ × (-2)^-1 × (a⁴m⁻⁴)¹
- 5a⁴ × -1/2 × a⁴ × m⁴
- -5/2 × a⁴ × a⁴ × m⁴
The next step is to apply the rule for multiplication of exponents with the same base which states that we add the exponents. However, as there are no like bases for multiplication here, we just multiply the coefficients.
The final simplified form is -5a⁸m⁴ / 2.