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

Insert the corresponding expression:

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

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 $9^{3x} \times 2^{3x}$.