Final answer:
To find the monomial, we need to multiply the given expressions and raise each expression to the indicated power. Then, we multiply the two expressions together to get the monomial.
Step-by-step explanation:
To find the monomial, we need to multiply the given expressions:
(-\(\frac{2}{3}x^2y\))^3(-\(\frac{3}{4}xy^2\))^2
To simplify, we raise each expression to the indicated power:
\((-\(\frac{2}{3}x^2y\))^3 = (-\(\frac{2}{3})^3)(x^2)^3(y)^3 = -\frac{8}{27}x^6y^3\)
\((-\(\frac{3}{4}xy^2\))^2 = (-\(\frac{3}{4})^2)(x)^2(y^2)^2 = \frac{9}{16}x^2y^4\)
Then, we multiply the two expressions together:
\((-\frac{8}{27}x^6y^3)(\frac{9}{16}x^2y^4) = (-\frac{8}{27})(\frac{9}{16})(x^6)(x^2)(y^3)(y^4) = -\frac{72}{432}x^8y^7\)
Therefore, the monomial is -\(\frac{72}{432}x^8y^7\).