Expand (9×11×2×7)^9: Product Raised to Power Expression

Question

Expand the following equation:

(9x11x2x7)9

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 According to the laws of exponents, a multiplication raised to a power (N)
00:08 equals the multiplication where each factor is raised to the same power (N)
00:14 This formula is valid regardless of how many factors are in the multiplication
00:21 We will apply this formula to our exercise
00:28 We'll break down the multiplication into each factor separately raised to the power (N)
00:39 This is one possible solution to the question
00:50 In multiplication, the order of factors doesn't matter
01:00 Therefore, we'll change the order of factors in order to determine the other solutions
01:14 This is another potential solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the expression to be expanded: (9×11×2×7)9(9 \times 11 \times 2 \times 7)^9
  • Step 2: Apply the Power of a Product rule: (a×b×c×d)n=an×bn×cn×dn(a \times b \times c \times d)^n = a^n \times b^n \times c^n \times d^n
  • Step 3: Distribute the power of 9 to each factor: 99×119×29×799^9 \times 11^9 \times 2^9 \times 7^9
  • Step 4: Recognize that due to the commutative property of multiplication, the order of factors is irrelevant.

Applying the Power of a Product rule:

(9×11×2×7)9=99×119×29×79(9 \times 11 \times 2 \times 7)^9 = 9^9 \times 11^9 \times 2^9 \times 7^9

This means that all given answer choices that represent this expression and its commutative orderings are correct solutions. Therefore, the solution to the problem is correctly all answers are equivalent.

Therefore, the correct answer to this problem is: All answers are correct.

Answer

All answers are correct