la multiplicación de los siguientes monomios l (ab^2)(-3a^3c)=-3a^3 (x^2y^2)(-0.5x^3y^2)=-0.3x^3 ((-m^2n)/(2))(4m^3n^2)= (2x)^2x= ((x)/(2))^3(-2y^4)= (-3pq^3)^2(2p^2q)= p. 5abtimes 2a^2b^4times 3ac= -0.5p^5qtimes (-1)/(2)q^3times 0.1pqr=

Vamos a resolver cada una de las multiplicaciones de monomios paso a paso:<br /><br />1. \((ab^{2})(-3a^{3}c)\)<br /> \[<br /> = -3a^{1+3}b^{2}c<br /> = -3a^{4}b^{2}c<br /> \]<br /><br />2. \((x^{2}y^{2})(-0.5x^{3}y^{2})\)<br /> \[<br /> = -0.5x^{2+3}y^{2+2}<br /> = -0.5x^{5}y^{4}<br /> \]<br /><br />3. \(\left(\frac{-m^{2}n}{2}\right)(4m^{3}n^{2})\)<br /> \[<br /> = \frac{-m^{2}n}{2} \cdot 4m^{3}n^{2}<br /> = -2m^{2+3}n^{1+2}<br /> = -2m^{5}n^{3}<br /> \]<br /><br />4. \((2x)^{2}x\)<br /> \[<br /> = (2x)^{2} \cdot x<br /> = 4x^{2} \cdot x<br /> = 4x^{3}<br /> \]<br /><br />5. \(\left(\frac{x}{2}\right)^{3}(-2y^{4})\)<br /> \[<br /> = \left(\frac{x}{2}\right)^{3} \cdot (-2y^{4})<br /> = \frac{x^{3}}{8} \cdot (-2y^{4})<br /> = -\frac{1}{4}x^{3}y^{4}<br /> \]<br /><br />6. \((-3pq^{3})^{2}(2p^{2}q)\)<br /> \[<br /> = (-3pq^{3})^{2} \cdot 2p^{2}q<br /> = 9p^{2}q^{6} \cdot 2p^{2}q<br /> = 18p^{4}q^{7}<br /> \]<br /><br />7. \(5ab \times 2a^{2}b^{4} \times 3ac\)<br /> \[<br /> = 5 \cdot 2 \cdot 3 \cdot a \cdot a^{2} \cdot b \cdot b^{4} \cdot ac<br /> = 30a^{1+2+1}b^{1+4}c<br /> = 30a^{4}b^{5}c<br /> \]<br /><br />8. \(-0.5p^{5}q \times \frac{-1}{2}q^{3} \times 0.1pqr\)<br /> \[<br /> = -0.5 \cdot \frac{-1}{2} \cdot 0.1 \cdot p^{5} \cdot q \cdot q^{3} \cdot pqr<br /> = 0.25 \cdot 0.1 \cdot p^{5+1+1} \cdot q^{1+3+1}<br /> = 0.025p^{7}q^{5}<br /> \]<br /><br />Por lo tanto, las respuestas correctas son:<br /><br />1. \(-3a^{4}b^{2}c\)<br />2. \(-0.5x^{5}y^{4}\)<br />3. \(-2m^{5}n^{3}\)<br />4. \(4x^{3}\)<br />5. \(-\frac{1}{4}x^{3}y^{4}\)<br />6. \(18p^{4}q^{7}\)<br />7. \(30a^{4}b^{5}c\)<br />8. \(0.025p^{7}q^{5}\)