16a^4c^5-12a^2c^4

To factor the expression \(16a^4c^5 - 12a^2c^4\), we start by identifying the common factors in both terms.

1. Identify the common coefficients and terms:

   • The coefficients are \(16\) and \(12\). The greatest common factor (GCF) of \(16\) and \(12\) is \(4\).
   • For \(a^4\) and \(a^2\), the common factor is \(a^2\).
   • For \(c^5\) and \(c^4\), the common factor is \(c^4\).

2. Factor out the GCF: The GCF of the entire expression is \(4a^2c^4\).

Now we can factor out \(4a^2c^4\) from the original expression:

\[ 16a^4c^5 - 12a^2c^4 = 4a^2c^4(4a^2c - 3) \]

Thus, the factored form of the expression is:

\[ \boxed{4a^2c^4(4a^2c - 3)} \]