Multiply Powers: Solve 8^7 × 8^8 × 9^7

Question

Insert the corresponding expression:

87×88×97= 8^7\times8^8\times9^7=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the power laws, a product raised to a power (N)
00:06 equals a product where each factor is raised to the same power (N)
00:15 Note which factors are raised to the same power
00:18 We'll apply this formula to our exercise
00:21 Place these factors inside of parentheses raised to the power (N)
00:31 This is the solution

Step-by-Step Solution

The goal is to express the given expression 87×88×978^7 \times 8^8 \times 9^7 using properties of exponents.

First, observe that 878^7 and 979^7 share a common exponent of 77. So, they can be factored as:

(8×9)7(8 \times 9)^7.

This handles the product 87×978^7 \times 9^7. Now, include 888^8 which is not part of the factoring:

(8×9)7×88(8 \times 9)^7 \times 8^8.

This resulting expression matches the provided possible choice.

Therefore, the rewritten expression is (8×9)7×88\left(8 \times 9\right)^7 \times 8^8.

Answer

(8×9)7×88 \left(8\times9\right)^7\times8^8