$\"\"$

First group the coefficients and variables.

4m⁴(n⁷m) = 4n⁷(m⁴·m)(Apply commutative property of multiplication: a × b = b × a) $\"\"$

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

= 4n⁷m^{4 + 1}

= 4n⁷m⁵ (Add exponents: 4 + 1 = 5) $\"\"$

The product of 4m⁴(n⁷m) is 4n⁷m⁵.