Final answer:
To divide (4b³)/(x) by (6b⁴x)/(5x⁴), we write it as a single fraction and simplify by dividing the coefficients, subtracting the exponents, and canceling out like terms. The simplified result is (10x³)/(3b).
Step-by-step explanation:
To divide (4b³)/(x) by (6b⁴x)/(5x⁴), we simplify the expression using the rules of division of exponentials. First, let's write this as a single fraction:
(4b³)/(x) ÷ (6b⁴x)/(5x⁴) = (4b³ × 5x⁴)/(x × 6b⁴x)
Next, we simplify the numerator and the denominator:
(4 × 5)b³x⁴/(6 × x × x)b⁴
We then simplify the coefficients and variables:
20b³x⁴/6xb⁴
Divide the coefficients (20/6 = 10/3) and subtract the exponents for 'b' (3 - 4 = -1, which means we'll move 'b' to the denominator) and cancel out the 'x' (since x⁴/x¹ = x³):
(10/3)b⁻¹x³
Finally, we have our simplified result:
(10b⁻¹x³)/3 or (10x³)/(3b)