Complete the Expression: (9×2)^(3x) Mathematical Pattern

Question

Insert the corresponding expression:

$\left(9\times2\right)^{3x}=$

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 (N)

00:11 We will apply this formula to our exercise

00:14 Note that all the factors in the multiplication operation are raised to the same exponent (N)

00:17 Therefore, we will raise each factor to this power (N)

00:20 This is the solution

To solve this problem, we'll apply the power of a product rule for exponents:

Identify that $(9 \times 2)^{3x}$ is a product of two numbers $9$ and $2$ raised to the same power $3x$ .
Apply the power of a product rule: $(ab)^n = a^n \times b^n$ .
In our case, $a = 9$ , $b = 2$ , and $n = 3x$ .
Thus, $(9 \times 2)^{3x} = 9^{3x} \times 2^{3x}$ .

Therefore, the expression $(9 \times 2)^{3x}$ simplifies to $9^{3x} \times 2^{3x}$ .

$9^{3x}\times2^{3x}$