\(a,5x^2y^4:\left(10x^2y\right)\\ =5x^2y^4.\dfrac{1}{10x^2y}\\ =\dfrac{5}{10}.\dfrac{x^2}{x^2}.\dfrac{y^4}{y}\\ =\dfrac{1}{2}y^3\)
\(b,\dfrac{3}{4}x^3y^3:\left(-\dfrac{1}{2}x^2y^2\right)\\ =\dfrac{3}{4}x^3y^3.\left(-\dfrac{2}{x^2y^2}\right)\\ =\dfrac{3}{4}.\left(-2\right).\dfrac{x^3}{x^2}.\dfrac{y^3}{y^2}\\ =-\dfrac{3}{2}xy\)
\(c,\left(-xy\right)^{10}:\left(-xy\right)^5=\left(-xy\right)^{10-5}=\left(-xy\right)^5=-x^5y^5\)
\(d,21xy^5z^3:\left(-7xy^2z^3\right)\\ =21xy^5z^3.\left(-\dfrac{1}{7xy^2z^3}\right)\\ =21.\left(-\dfrac{1}{7}\right).\dfrac{x}{x}.\dfrac{y^5}{y^2}.\dfrac{z^3}{z^3}\\ =-3y^3\)
a: =5/10*x^2:x^2*y^4:y=1/2y^3
b: =(3/4:(-1/2))*x^3:x^2*y^3:y^2
=-3/2xy
c: =(-xy)^10-5=(-xy)^5=-x^5y^5
d: \(=\dfrac{21}{-7}\cdot x:x\cdot\dfrac{y^5}{y^2}\cdot\dfrac{z^3}{z^3}=-3y^3\)