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

Question

Insert the corresponding expression:

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

00:09 Let's simplify this problem together.

00:12 Based on the rules of exponents, a product in parentheses raised to the power of N

00:18 is like saying each number in the product is raised to the power of N.

00:23 We'll use this rule to solve our exercise.

00:26 Remember, each part of the product gets the power of N.

00:32 And that's how we find 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.

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