Complete the Expression: Writing (ax×3)^b in Standard Form

To solve this problem, we need to apply the Power of a Product Rule, which states that if you raise a product to an exponent, you raise each factor in the product to that exponent.

We start with the expression $(a \times x \times 3)^b$. By applying the Power of a Product Rule, we can rewrite it as:

• Raise $a$ to the power of $b$, giving us $a^b$.
• Raise $x$ to the power of $b$, giving us $x^b$.
• Raise $3$ to the power of $b$, giving us $3^b$.

Therefore, the expression $(a \times x \times 3)^b$ becomes $a^b \times x^b \times 3^b$. This matches choice 3 from the provided options.

This demonstrates the proper application of the Power of a Product Rule. Thus, the expression is simplified to:

$a^b \times x^b \times 3^b$.