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

Insert the corresponding expression:

(3×6×4)2a= \left(3\times6\times4\right)^{2a}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

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1

Understand the problem

Insert the corresponding expression:

(3×6×4)2a= \left(3\times6\times4\right)^{2a}=

2

Step-by-step solution

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

(3×6×4)2a=32a×62a×42a (3 \times 6 \times 4)^{2a} = 3^{2a} \times 6^{2a} \times 4^{2a}

This expression tells us that the exponent 2a2a is distributed to each factor inside the parentheses.

Therefore, the correct answer is 32a×62a×42a3^{2a} \times 6^{2a} \times 4^{2a}, corresponding to choice C.

3

Final Answer

32a×62a×42a 3^{2a}\times6^{2a}\times4^{2a}

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\( (4^3)^2= \)

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