Simplify the Product: 3^x × 7^x × 5^x Using Exponent Rules

Question

Insert the corresponding expression:

$3^x\times7^x\times5^x=$

00:00 Simplify the following problem

00:03 According to the laws of exponents, a product raised to the power (N)

00:07 Equals a product where each factor is raised to the same power (N)

00:12 We will apply this formula to our exercise

00:15 Note that each factor is raised to the same power (N)

00:23 This is the solution

To solve this problem, follow these steps:

Step 1: Identify the expression provided: $3^x \times 7^x \times 5^x$ .
Step 2: Apply the exponent rule for powers of a product: when multiple terms with the same exponent are multiplied, they can be combined under one power. This gives us: $(3 \times 7 \times 5)^x$ .

Therefore, the simplified expression is $\left(3 \times 7 \times 5\right)^x$ , which matches our final result.

$\left(3\times7\times5\right)^x$