Final answer:
The product of the expressions (3x + 5 / y^6) * (4y^3 / 5) is calculated by multiplying the numerators and denominators. After canceling out common factors, the final simplified product is 12x/y^3.
Step-by-step explanation:
The product of the expressions given is (3x + 5 / y^6) * (4y^3 / 5). To find the product, you multiply the numerators together and the denominators together. Since y ≠ 0, we start by simplifying the fractions.
Multiplying the numerators: 3x * 4y^3 = 12xy^3
Multiplying the denominators: y^6 * 5 = 5y^6
Then, we simplify the equation by canceling out common factors. Here, the 5 in the numerator and denominator cancel each other out. After cancellation, our expression becomes:
Simplified product: 12xy^3 / y^6
Finally, we apply the rules for dealing with exponents when we have the same base:
Final answer: 12x/y^3