First group the coefficients and variables.

(10x)(4x⁴) = (10 · 4) (x · x⁴)

=  (40) (x · x⁴)            (Multiply: 10 · 4 = 40)

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

=  (40) (x^{1 + 4})    

=  40x⁵                        (Add exponents: 1 + 4 = 5)

 Product of  (10x)(4x⁴) is 40x⁵.