Complete the Expression: (3×6×4)^(2a) Power Operation

Question

Insert the corresponding expression:

$\left(3\times6\times4\right)^{2a}=$

00:00 Simplify the following problem

00:04 In order to open parentheses with a multiplication operation and an outside exponent

00:08 Raise each factor to the power

00:15 We will apply this formula to our exercise

00:19 Note that all the factors in the multiplication operation have the same exponent (N)

00:24 Therefore we will raise each factor to this power

00:30 This is the solution

To simplify the expression $(3 \times 6 \times 4)^{2a}$ , we apply the power of a product rule:

$(3 \times 6 \times 4)^{2a} = 3^{2a} \times 6^{2a} \times 4^{2a}$

This expression tells us that the exponent $2a$ is distributed to each factor inside the parentheses.

Therefore, the correct answer is $3^{2a} \times 6^{2a} \times 4^{2a}$ , corresponding to choice C.

$3^{2a}\times6^{2a}\times4^{2a}$