Expand (2·6·3)^9: Step-by-Step Product Power Calculation

Question

Choose the expression that corresponds to the following:

$\left(2\cdot6\cdot3\right)^9=$

00:00 Simplify the following problem

00:03 When we are presented with a multiplication operation where all the factors have the same exponent (N)

00:08 Each factor can be raised to the power (N)

00:12 We'll apply this formula to our exercise

00:23 Let's proceed to review the incorrect options

00:29 This option is incorrect due to the fact that factor 2 is not raised to the power

00:40 The same thing with this option but with factor 3

00:46 And this one with factor 6

00:53 This is the solution

To solve this problem, let's expand the expression $(2 \cdot 6 \cdot 3)^9$ .

Step 1: Apply the power of a product rule: $(a \cdot b \cdot c)^n = a^n \cdot b^n \cdot c^n$ .

Step 2: Identify the factors. In this case, we have three factors: $2$ , $6$ , and $3$ .

Step 3: Apply the exponent 9 to each factor:

Step 4: Combine these into the fully expanded form:

$2^9 \cdot 6^9 \cdot 3^9$ .

Review the answer options and note that there is no choice that matches this correct form.

Therefore, none of the answer choices are correct.

None of the answers are correct.