Final answer:
To simplify the expression (-3x^3yz^4)^(-2)(y^2z), we need to apply the rule for raising a power to a power. The final simplified expression is (yz^8)/(9x^6).
Step-by-step explanation:
To simplify the expression (-3x^3yz^4)^(-2)(y^2z), we need to apply the rule for raising a power to a power. The rule states that when we raise an exponent to another exponent, we multiply the exponents. In this case, we have (-3x^3yz^4)^(-2), so we need to multiply the exponents of the variables inside the parentheses by -2. Applying this rule, we get (-3^(-2))(x^(3*(-2)))(y^(-1*(-2)))(z^(4*(-2))). Simplifying further, we get (1/(9x^(-6)))(1/(y^2))(1/(z^(-8))). Now, multiplying this expression by y^2z, we can combine like terms by adding the exponents. Thus, the final simplified expression becomes 1/(9x^(-6)yz^(-8)). To write it using only positive exponents, we can move the terms in the denominator to the numerator by changing the signs of the exponents. Therefore, the final answer is (yz^8)/(9x^6).