First group the coefficients and variables.

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

= (4 · 5) (a · a²) (b · b³) (Apply 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 1 + 3 = 4)

=  20a³b⁴

The product of (4ab)(5a²b³) is 20a³b⁴.