what is the greatest common monomial factor of 6x^2y^3z^4-4x^3y^3z^3+10xy^3z^4
To find the greatest common monomial factor of the given expression, we need to identify the highest power of each variable that is common to all the terms. Let's break down the expression:
6x^2y^3z^4 - 4x^3y^3z^3 + 10xy^3z^4
First, let's look at the variable x. The highest power of x that is common to all the terms is x^2.
Next, let's consider the variable y. The highest power of y that is common to all the terms is y^3.
Finally, let's examine the variable z. The highest power of z that is common to all the terms is z^3.
Therefore, the greatest common monomial factor of the expression is x^2y^3z^3.