Complete the Expression: Finding (4×a)^(2b) in Exponential Form

To solve this problem, we'll follow these steps:

• Step 1: Identify the structure and components of the initial expression
• Step 2: Apply the inverse power of a power rule
• Step 3: Find the matching choice among the given options

Now, let's work through each step:

Step 1: The given expression is $\left(4 \times a\right)^{2b}$. This indicates that the base $\left(4 \times a\right)$ is raised to the power of $2b$.

Step 2: By the inverse power of a power property, we rewrite $\left(4 \times a\right)^{2b}$ in a way that exposes it as a power raised to a power. The expression $(x^{m \cdot n})$ equates to $(x^m)^n$. Hence, we can rewrite $\left(4 \times a\right)^{2b}$ as $\left(\left(4 \times a\right)^2\right)^b$.

Step 3: The correct answer from the provided choices matches choice 1: $\left(\left(4 \times a\right)^2\right)^b$.

Therefore, applying the inverse power of a power rule, the expression $\left(4 \times a\right)^{2b}$ becomes $\left(\left(4 \times a\right)^2\right)^b$.