Final answer:
The expression that is not equivalent to (4n/3m⁵)−² is option d. 1/(4n/3m⁵)². The equivalent expressions are a. 9m¹⁰/16n², b. 16n²/9m¹⁰, and c. 4n/3m⁵
Step-by-step explanation:
The expression that is not equivalent to (4n/3m⁵)−² is option d. 1/(4n/3m⁵)².
To see which expressions are equivalent to (4n/3m⁵)−², we need to simplify the expression. We can rewrite (4n/3m⁵)−² as (3m⁵/4n)². Squaring a fraction means squaring the numerator and the denominator independently. So, (3m⁵/4n)² = (3m⁵)² / (4n)² = 9m¹⁰/16n². Therefore, option a. 9m¹⁰/16n² is the simplified expression that is equivalent to (4n/3m⁵)−².
Option b. 16n²/9m¹⁰ and option c. 4n/3m⁵ are also equivalent to (4n/3m⁵)−² after simplification.