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.

00:12 Let's make this problem simpler, step by step!

00:16 We'll start by solving the product of numbers.

00:22 When you multiply powers with the same base,

00:26 Add the exponents together, like this: A to the power of M plus N.

00:32 So, let's use this rule and add the powers in our problem.

00:49 Now, we factor out the common term from the brackets.

01:00 Great job! That's how we find 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 $4a^7(a^7 + 5)$ .

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