a)

$2a\cdot 3b=2\cdot 3\cdot a\cdot b=6ab$

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b)

$6cd\cdot \left(-2\right)d=6\cdot \left(-2\right)\cdot c\cdot d\cdot d=-12c{d}^2$

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c)

$3x^2{y}^2\cdot 13y^3{x}^5=3\cdot 13\cdot x^2\cdot x^5\cdot y^2\cdot y^3=39x^7{y}^5$

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d)

$5a^{2}b\cdot \left(-7a^9{c}^2\right)=5\cdot \left(-7\right)\cdot a^2\cdot a^9\cdot b\cdot c^2=-35a^{11}b{c}^2$

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e)

$1\frac{1}{3}{x}^{7}z\cdot \frac{1}{4}{z}^{7}y=\frac{\cancel{4}}{3}\cdot \frac{1}{\cancel{4}}\cdot x^7\cdot y\cdot z\cdot x^7=\frac{1}{3}{x}^{7}y{z}^8$

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f)

$2b^{2}a\cdot \left(-3,5a^{3}b\right)\cdot \left(-\frac{1}{7}ab\right)=2\cdot \left(-3,5\right)\cdot \left(-\frac{1}{7}\right)\cdot a\cdot a^3\cdot a\cdot b^2\cdot b\cdot b=$

$=-\cancel{7}\cdot \left(-\frac{1}{\cancel{7}}\right)\cdot a^5\cdot b^4=1a^5{b}^4=a^5{b}^4$