Final answer:
The value of 12x²y⁴z³÷(2xy²*3yz²) simplifies to 2xy²zxyz by dividing the coefficients and subtracting the exponents of like bases. To divide 12x²y⁴z³ by (2xy² * 3yz²), simplify by cancelling out the common factors in the numerator and denominator to get 6xyz.
Step-by-step explanation:
To divide 12x²y⁴z³ by (2xy² * 3yz²), we can simplify the expression by cancelling out the common factors in the numerator and denominator. The common factors are 2, x, y², and z². Cancelling them out, we get:
(12x²y⁴z³) / (2xy² * 3yz²) = (6^1 * x^(2-1) * y^(4-2) * z^(3-2)) / (1 * 1 * 3 * 1) = 6xyz
So, the value of the expression is 6xyz.