Simplify the Expression: 7⁵ × 2³ × 7² × 2⁴ Product of Powers

Simplify the following equation:

$7^5\times2^3\times7^2\times2^4=$

Video Solution

Solution Steps

00:00 Simply

00:03 We'll use the commutative law and arrange equal bases together

00:16 We'll use the formula for multiplying power by power

00:18 Any number (A) to the power of (M) multiplied by the same number (A) to the power of (N)

00:21 We'll get the same number (A) to the power of the sum of exponents (M+N)

00:24 We'll use this formula in our exercise

00:27 And we'll equate the numbers with the variables in the formula

00:37 We'll keep the base and add the exponents

01:04 We'll use the same method for the second base

01:28 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll apply the laws of exponents to simplify the expression $7^5 \times 2^3 \times 7^2 \times 2^4$ .

Let's follow these steps:

Step 1: Identify like bases.
We have two like bases in the expression: 7 and 2.
Step 2: Apply the product of powers rule for each base separately.
For the base 7: $7^5 \times 7^2 = 7^{5+2} = 7^7$ .
For the base 2: $2^3 \times 2^4 = 2^{3+4} = 2^7$ .
Step 3: Combine the results.
The expression simplifies to $7^7 \times 2^7$ .

The simplified form of the original expression is therefore $7^7 \times 2^7$ .