Final answer:
To divide and simplify the expression 8a³x⁵/9x by 4a/3x, multiply by the reciprocal and simplify, resulting in (2/3)a²x⁴. The final simplified expression is thus (2/3)a²x⁴.
Step-by-step explanation:
The question involves the division of two algebraic expressions and simplifying the result. To Divide the expression 8a³x⁵/9x by 4a/3x, we need to multiply the first expression by the reciprocal of the second expression. Simplifying expressions involves reducing them to their most basic form by combining like terms and reducing any numerical coefficients.
First, write the problem as a multiplication of reciprocals:
(8a³x⁵/9x) × (3x/4a) = (8 × 3)/(9 × 4) × a³/a × x⁵/x
Now, simplify the numerical coefficients by multiplying 8 and 3 and then dividing by the product of 9 and 4. We also need to subtract the exponents of the like terms (a's and x's) as per the laws of exponents.
The simplified form of the numerical coefficient is 24/36, which can be further simplified to 2/3. For the variables, subtract the exponents of like bases to get a²x⁴.
The final simplified expression is thus (2/3)a²x⁴.