¡Claro! Resolveré cada una de las multiplicaciones paso a paso:
### 1. [tex]\(1(-3a) \left(a^2\right)\)[/tex]
[tex]\[ 1 \cdot (-3a) \cdot a^2 = -3a \cdot a^2 = -3a^3 \][/tex]
### 2. [tex]\(\left(3x^2\right)\left(-x^3n\right)\)[/tex]
[tex]\[ 3x^2 \cdot (-x^3n) = 3 \cdot (-1) \cdot x^{2+3} \cdot n = -3x^5n \][/tex]
### 3. [tex]\(\left(-m^2n\right)\left(-3m^2\right)\)[/tex]
[tex]\[ (-m^2n) \cdot (-3m^2) = (-1) \cdot (-3) \cdot m^{2+2} \cdot n = 3m^4n \][/tex]
### 4. [tex]\((-5a^3y^2)\left(ay^2\right)\)[/tex]
[tex]\[ -5a^3y^2 \cdot ay^2 = -5 \cdot a^{3+1} \cdot y^{2+2} = -5a^4y^4 \][/tex]
### 5. [tex]\((-2ab)\left(-3a^2b^3\right)\)[/tex]
[tex]\[ (-2ab) \cdot (-3a^2b^3) = (-2) \cdot (-3) \cdot a^{1+2} \cdot b^{1+3} = 6a^3b^4 \][/tex]
### 6. [tex]\(\left(\frac{1}{2}x^3\right)\left(-\frac{2}{3}a^2x\right)\)[/tex]
[tex]\[ \left(\frac{1}{2}x^3\right) \cdot \left(-\frac{2}{3}a^2x\right) = \frac{1}{2} \cdot -\frac{2}{3} \cdot a^2 \cdot x^{3+1}\][/tex]
[tex]\[ = -\frac{2}{6}a^2x^4 = -\frac{1}{3}a^2x^4 \][/tex]
### 7. [tex]\(\left(\frac{2}{3}a^5\right)\left(\frac{2}{4}a^2b^4\right)\)[/tex]
[tex]\[ \left(\frac{2}{3}a^5\right) \cdot \left(\frac{2}{4}a^2b^4\right) = \frac{2}{3} \cdot \frac{1}{2} \cdot a^{5+2} \cdot b^4 = \frac{2 \cdot 1}{3 \cdot 2} a^7b^4\][/tex]
[tex]\[ = \frac{1}{3}a^7b^4 \][/tex]
### 8. [tex]\(8\left(-\frac{3}{5}m^2\right)\left(-5a^2m\right)\)[/tex]
[tex]\[ 8 \cdot \left(-\frac{3}{5}m^2\right) \cdot \left(-5a^2m\right) = 8 \cdot -\frac{3}{5} \cdot -5 \cdot a^2 \cdot m^{2+1} \][/tex]
[tex]\[ = 8 \cdot \frac{15}{5} \cdot a^2 m^3 = 8 \cdot 3 \cdot a^2 m^3 = 24a^2m^3 \][/tex]
### 9. [tex]\(q\left(-\frac{1}{2}x^2y\right)\left(-\frac{3}{5}xy^2\right)\)[/tex]
[tex]\[ q \cdot \left(-\frac{1}{2}x^2y\right) \cdot \left(-\frac{3}{5}xy^2\right) = q \cdot -\frac{1}{2} \cdot -\frac{3}{5} \cdot x^{2+1} \cdot y^{1+2} \][/tex]
[tex]\[ = q \cdot \frac{3}{10} \cdot x^3y^3 = \frac{3}{10}q x^3y^3 \][/tex]
### 10. [tex]\(0\left(-\frac{10}{3}x^3\right)\left(-\frac{3}{4}x^2y\right)\)[/tex]
[tex]\[ 0 \cdot \left(-\frac{10}{3}x^3\right) \cdot \left(-\frac{3}{4}x^2y\right) = 0 \][/tex]
En resumen, las soluciones son:
[tex]\[
\begin{array}{cc}
-3a^3, & -3n x^5, \\
3m^4 n, & -5a^4 y^4, \\
6a^3b^4, & -\frac{1}{3}a^2x^4, \\
\frac{1}{3}a^7b^4, & 24a^2m^3, \\
0.3qx^3y^3, & 0
\end{array}
\][/tex]
