a) \(-x^3y\cdot\left(-2xy\right)\)
\(=\left(-1\cdot-2\right)\cdot\left(x^3\cdot x\right)\cdot\left(y\cdot y\right)\)
\(=2\cdot x^{3+1}\cdot y^{1+1}\)
\(=2x^4y^2\)
b) \(\left(-4x^2\right)^2y^3\cdot\left(-\dfrac{3}{4}x\right)\)
\(=\left(-4\right)^2\cdot\left(x^2\right)^2\cdot y^3\cdot\left(-\dfrac{3}{4}\right)\)
\(=16x^4y^3\cdot\left(-\dfrac{3}{4}x\right)\)
\(=\left(16\cdot-\dfrac{3}{4}\right)\cdot\left(x^4\cdot x\right)\cdot y^3\)
\(=-12x^5y^3\)
c) \(\left(-2x^2y^3\right)\left(-\dfrac{1}{2}xy^2\right)^3\)
\(=\left(-2x^2y^3\right)\cdot\left(-\dfrac{1}{2}\right)^3\cdot x^3\cdot\left(y^2\right)^3\)
\(=\left(-2x^2y^3\right)\cdot\left(-\dfrac{1}{8}x^3y^6\right)\)
\(=\left(-2\cdot-\dfrac{1}{8}\right)\cdot\left(x^2\cdot x^3\right)\cdot\left(y^3\cdot y^6\right)\)
\(=\dfrac{1}{4}x^5y^9\)
d) \(\left(-\dfrac{4}{5}x^4y^2\right)\cdot\left(-3x^2y^5\right)\)
\(=\left(-\dfrac{4}{5}\cdot-3\right)\cdot\left(x^4\cdot x^2\right)\cdot\left(y^2\cdot y^5\right)\)
\(=\dfrac{4\cdot3}{5}\cdot x^{4+2}\cdot y^{5+2}\)
\(=\dfrac{12}{5}x^6y^7\)
a, \(2x^4y^2\)
b, \(12x^5y^3\)
c, \(\dfrac{1}{4}x^5y^9\)
d, \(\dfrac{12}{5}x^6y^7\)
