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

Question

$4a^2\times a^4\times a^5\times a^3+20a^7=$

Simplify the expression as much as possible.

00:00 Simplify the following problem

00:03 Let's solve the product of numbers first

00:10 When multiplying powers with equal bases

00:13 The power of the result equals the sum of powers

00:17 We'll apply this formula to our exercise and add together the powers

00:37 Let's factor out the common term from the parentheses

00:48 This is the solution

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 $4a^7(a^7 + 5)$ .

$4a^7(a^7+5)$