First group the coefficients and variables.

(4ab)(5a²b³) = ( 4 · 5) (a · b · a² · b³)

=  ( 4 · 5) (a · a²) (b · b³)     (Commutative property of multiplication: a × b = b × a)

=  ( 20) (a · a²) (b · b³)        (Multiply: 4 × 5 = 20)

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

=  ( 20) (a^{1+ 2} ) (b^{1 + 3})

=  ( 20) (a³ ) (b⁴)                 (Add exponents: 1 + 2 = 3 and 3 + 4 = 7)

=  20a³b⁴ \ \ Product of  Product of (4ab)(5a²b³) is 20a³b⁴.