Final answer:
The product of the rational expressions 3x/4 and 8/9 is simplified to 2x/3 after multiplying the numerators and denominators and then simplifying by canceling common factors.
Step-by-step explanation:
Finding the Product of Rational Algebraic Expressions
To find the product of 3x/4 and 8/9, you need to multiply the numerators together and the denominators together, simplifying any common factors as needed. First, multiply the numerators: 3x × 8 = 24x. Then, multiply the denominators: 4 × 9 = 36. The resulting fraction is 24x/36.
Now, simplify by canceling out the common factors. Both 24 and 36 are divisible by 12, so divide the numerator and the denominator by 12. The simplified product is 2x/3.