Solve: 4^a × 8^a × 2^a - Multiplying Powers with Same Exponent

Question

Insert the corresponding expression:

4a×8a×2a= 4^a\times8^a\times2^a=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, a product raised to a power (N)
00:07 Equals a product where each factor is raised to the same power (N)
00:10 We will apply this formula to our exercise
00:13 Note that each factor is raised to the same power (N)
00:22 This is the solution

Step-by-Step Solution

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

  • Step 1: Identify the common exponent in all terms.

  • Step 2: Apply the power of a product rule to combine the terms.

Now, let's work through each step:
Step 1: We have the expression 4a×8a×2a 4^a \times 8^a \times 2^a , where each base is raised to the same power, a a .
Step 2: Using the power of a product rule, we can combine the terms into a single expression: (4×8×2)a (4 \times 8 \times 2)^a .
Therefore, in terms of the choice list, the corresponding expression is (4×8×2)a \left(4\times8\times2\right)^a , which is choice 2.

Answer

(4×8×2)a \left(4\times8\times2\right)^a