Final answer:
To simplify the expression (9bx)/(2x⁴) × (8x)/(3b), multiply the numerators and denominators, then cancel common factors to get a simplified answer of 12/x².
Step-by-step explanation:
To multiply and simplify the expression (9bx)/(2x⁴) × (8x)/(3b), we follow the steps of multiplying the numerators and denominators together, then simplifying by canceling common factors.
The multiplication of the numerators gives us 9bx × 8x, which equals 72bx². For the denominators, 2x⁴ × 3b yields 6bx⁴. Now we place the numerators over the denominators:
72bx² / 6bx⁴
Next, we simplify by canceling out the common factors. The b's cancel out, and we can divide both 72 and 6 by 6 to get 12. We also subtract the exponents of x according to the rules of exponents which gives us x² - x⁴ = x⁻².
The simplified expression is therefore 12/x².