Final answer:
To simplify (12x^(9)y^(4))/(6x^(3)y^(3)), divide the coefficients and subtract the exponents of like bases to get 2x^(6)y^(2). The correct answer is option D, which is 2x^(6)y^(2).
Step-by-step explanation:
To find the expression equivalent to (12x9y4) / (6x3y3), we need to simplify the expression by dividing the terms in the numerator by the corresponding terms in the denominator. Assuming the denominators are not zero, the rules of exponents allow us to simplify the given expression as follows:
We can divide the coefficients (numbers in front of the variables) and subtract the exponents of like bases. This results in:
2x9-3y4-3 = 2x6y
Therefore, the equivalent expression is option D, which is 2x6y2.
Complete question is:
Which expression is equivalent to the given expression? Assume the denominator does not equal zero. (12x^(9)y^(4))/(6x^(3)y^(3))
A. 2x^(3)y^(2)
B. (2)/(x^(6)y^(2))
C. (2)/(x^(3)y^(2))
D. 2x^(6)y^(2)