Simplify the Expression: a⁴ × b⁴ Product of Powers

Insert the corresponding expression:

$a^4\times b^4=$

Video Solution

Solution Steps

00:07 Let's simplify this problem together.

00:11 When you multiply numbers, each raised to a power, N, you can rewrite it as all numbers in parentheses, then raise them to power, N.

00:21 We'll use this method in our exercise now.

00:24 Great work, let's see how this formula solves our problem.

00:28 And that's how we find the solution!

Step-by-Step Solution

To solve the problem, we need to simplify the expression $a^4 \times b^4$ to a single power using exponent rules.

Here’s a step-by-step explanation:

Step 1: Identify the expression that needs simplification: $a^4 \times b^4$ .
Step 2: Apply the exponent rule called the power of a product: $(x \times y)^n = x^n \times y^n$ .
Step 3: We can reverse this property. If we have $x^n \times y^n$ , we can combine it as $(x \times y)^n$ .
Step 4: Apply this to our expression: $a^4 \times b^4 = (a \times b)^4$ . Using the power of a product, $a^4 \times b^4 = (a \times b)^4$ .

Thus, the expression $a^4 \times b^4$ simplifies to $(a \times b)^4$ .