First group the coefficients and variables.

ab⁵ ·  8a²b⁵ = (1 · 8) (a · a²) (b⁵ · b⁵)

=  8 (a · a²) (b⁵ · b⁵)           (Multiply: 1 · 8 = 8)

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

=  8 (a^{1 + 2}) (b^{5 + 5})   

=  8a³b¹⁰                      (Add exponents: 1 + 2 = 3 and 5 + 5 = 10)

 Product of  ab⁵ ·  8a²b⁵ is 8a³b¹⁰.