First group the coefficients and variables.

3a² · 5a² = ( 3 · 5) (a² · a²)

=  ( 15) (a² · a²)           (Multiply:   3 · 5 =  15)

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

=  (15) (a^{2 + 2})

=  15a⁴                        (Add exponents: 2 + 2 = 4)

Product of  3a² · 5a²is 15a⁴  .