Final answer:
To simplify the given expression (-x² yz²)(-2x³ y³ z)², multiply the coefficients, add the exponents of the variables with the same base, and square the result to obtain 4x^10y^8z^6.
Step-by-step explanation:
To simplify the given expression, we will use the properties of exponents. Let's break down the expression step by step:
(-x² yz²)(-2x³ y³ z)²
First, multiply the coefficients: (-1)(-2) = 2
Next, multiply the variables with the same base by adding their exponents: x² * x³ = x^(2+3) = x^5, y * y³ = y^(1+3) = y^4, and z^2 * z = z^(2+1) = z^3
Finally, square the result: 2x^5y^4z^3 * 2x^5y^4z^3 = 4x^10y^8z^6
Therefore, the simplified expression is 4x^10y^8z^6.