Complete the Expression: (9×7×4) Raised to Power a

Question

Insert the corresponding expression:

(9×7×4)a= \left(9\times7\times4\right)^a=

Video Solution

Solution Steps

00:00 Simplify the following expression
00:04 In order to open parentheses with a multiplication operation and an outside exponent
00:08 We raise each factor to the power
00:13 We'll apply this formula to our exercise
00:22 This is the solution

Step-by-Step Solution

To solve this problem, let's apply the rule for the power of a product, which states that when a product is raised to a power, each factor is raised to that power.

  • Step 1: Write down the expression: (9×7×4)a(9 \times 7 \times 4)^a.
  • Step 2: Apply the power of a product rule: (x×y×z)n=xn×yn×zn(x \times y \times z)^n = x^n \times y^n \times z^n.
  • Step 3: Raise each factor in the expression to the power aa.
  • Step 4: Simplify the individual expressions: 9a×7a×4a9^a \times 7^a \times 4^a.

Thus, the expression (9×7×4)a(9 \times 7 \times 4)^a simplifies to 9a×7a×4a9^a \times 7^a \times 4^a.

The correct answer is 9a×7a×4a9^a \times 7^a \times 4^a, which corresponds to choice 2.

Answer

9a×7a×4a 9^a\times7^a\times4^a