First group the coefficients and variables.

10x³y(– 2xy²) = (10 · – 2) (x³ · x) (y · y²)

=  (– 20) (x³ · x) (y · y²)            (Multiply: 10 – 2 = – 20)

Since base is common, apply the product of powers property: a^m · aⁿ = a^{m + n}.

=  (– 20) (x^{3 + 1}) (y^{1 + 2} )

=  – 20x⁴y³                        (Add exponents: 3 + 1 = 4 and 1 + 2 = 3)

Product of  (10x³y)(– 2xy²) is  – 20x⁴y³.