Evaluate (a×3)³: Expanding the Cube of a Product

Insert the corresponding expression:

$\left(a\times3\right)^3=$

To solve the problem $(a \times 3)^3$, we'll apply the power of a product rule which states that $(x \cdot y)^n = x^n \cdot y^n$.

Step 1: Identify the individual factors within the parentheses. In this expression, $a$ and 3 are multiplied together and are being raised to the power of 3.

Step 2: Apply the power of a product property: Distribute the exponent of 3 to both $a$ and 3 inside the parentheses. We do so as follows:
$(a \times 3)^3 = a^3 \times 3^3$

Step 3: Express the result clearly. The expression simplifies to:
$a^3 \times 3^3$.

Therefore, the correct answer to this problem is $a^3 \times 3^3$.