Final Answer:
“(7x²) / (5y³z³)” is the equivalent expression of “((42x - 4y) * 10z³) / (6x²y⁻2)”, thus the correct option is c.
Step-by-step explanation:
When two expressions are equivalent, they are equal to each other. To find out if two expressions are equivalent, we can simplify both sides of the equation. To simplify the given expression, we can use the properties of exponents and combine like terms. First, we can combine the terms in the numerator to get “7x³”. Next, we can combine the terms in the denominator to get “5y³z³”. Therefore, the equivalent expression is “(7x²) / (5y³z³)”.
To check if the two expressions are equivalent, we can also use the distributive property. By expanding the original expression, we can see that it is equal to “(42x³ - 4x²y - 40x²y²z³ + 4xy³z³) / (6x²y⁻²)”. Similarly, if we expand “(7x²) / (5y³z³)”, we get the same expression. This shows that the two expressions are equal and hence, equivalent.
In conclusion, “(7x²) / (5y³z³)” is the equivalent expression of “((42x - 4y) * 10z³) / (6x²y⁻2)”.