Simplify the Expression: a⁴ × b⁴ Product of Powers

Question

Insert the corresponding expression:

$a^4\times b^4=$

00:00 Simplify the following problem

00:04 A multiplication where each factor is raised to its own power (N)

00:09 Can be converted to parentheses of the entire multiplication raised to the power of the factor (N)

00:13 We will apply this formula to our exercise

00:18 This is the 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 $(a \times b)^4$ .

$\left(a\times b\right)^4$