Solve: 8²⁵ × 7²⁵ × 10²⁵ × 5²⁵ Expression with Common Exponents

Question

Insert the corresponding expression:

$8^{25}\times7^{25}\times10^{25}\times5^{25}=$

00:00 Simplify the following problem

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

00:08 Equals a product where each factor is raised to that same power (N)

00:12 This formula is valid regardless of how many factors are in the product

00:19 We will apply this formula to our exercise

00:22 We will break down the product into each factor separately raised to the power (N)

00:34 This is the solution

To solve this problem, we'll apply the power of a product rule to the given expression:

Step 1: Recognize that each term $8^{25}$ , $7^{25}$ , $10^{25}$ , and $5^{25}$ is raised to the same power of 25.

Step 2: Use the rule $a^m \times b^m \times c^m \times d^m = (a \times b \times c \times d)^m$ .

Step 3: Combine the expression: $(8 \times 7 \times 10 \times 5)^{25}$ .

Therefore, the simplified expression is $\left(8 \times 7 \times 10 \times 5\right)^{25}$ .

This matches choice 1 from the provided options.

$\left(8\times7\times10\times5\right)^{25}$