Simplify the Expression: 4a^2 * a^4 * a^5 * a^3 + 20a^7

In order to simplify the expression $4a^2 \times a^4 \times a^5 \times a^3 + 20a^7$, we'll follow these steps:

• Step 1: Combine the powers of $a$ in the first term using the product of powers rule:
  $4a^2 \times a^4 \times a^5 \times a^3 = 4a^{2+4+5+3} = 4a^{14}$.

• Step 2: Rewrite the given expression with the simplified first term:
  $4a^{14} + 20a^7$.

• Step 3: Identify and factor out the greatest common factor (GCF) from the expression:
  Both terms have $4a^7$ as a common factor. Factor this out:
  $4a^{14} + 20a^7 = 4a^7(a^7) + 4a^7(5) = 4a^7(a^7 + 5)$.

Therefore, the simplified form of the expression is $4a^7(a^7 + 5)$.