The problem asks us to simplify the expression $(a^2 b^3)(4 a^4 b^3)$.

1. Problem Description

The problem asks us to simplify the expression $(a^2 b^3)(4 a^4 b^3)$.

2. Solution Steps

First, we can rewrite the expression by grouping like terms:

$(a^2 b^3)(4 a^4 b^3) = 4 (a^2 a^4)(b^3 b^3)$

Next, we use the property of exponents that states $x^m x^n = x^{m+n}$. Applying this to the expression, we get:

$4 (a^2 a^4)(b^3 b^3) = 4 a^{2+4} b^{3+3}$

$4 a^{2+4} b^{3+3} = 4 a^6 b^6$

3. Final Answer

$4a^6b^6$