Final answer:
To divide the expression (2y)/(3x) ÷ (4y³)/(9xy), multiply by the reciprocal of the denominator and simplify by canceling out common factors in the numerators and denominators. The final answer is 3x / 2y².
Step-by-step explanation:
To divide the expression (2y)/(3x) ÷ (4y³)/(9xy), we can simplify the division of fractions by multiplying by the reciprocal of the denominator. The reciprocal of (4y³)/(9xy) is (9xy)/(4y³). So, the division becomes (2y)/(3x) × (9xy)/(4y³).
To simplify this, we can cancel out common factors in the numerators and denominators. Canceling out y from the numerator and denominator, and 3 from the numerator and denominator, we get (2)/(1x) × (3x)/(4y²).
Finally, multiplying the numerators and denominators, we get (2)(3x) / (1x)(4y²), which simplifies to 6x / 4y², or 3x / 2y².