Complete the Expression: Writing 10^3x in Standard Form

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

• Step 1: Understand the expression $10^{3x}$.
• Step 2: Apply the power of a power rule to rewrite it.
• Step 3: Identify the correct equivalent expression from the options.

Now, let's work through each step:
Step 1: The expression given is $10^{3x}$, which involves a base of 10 and a combination of numerical and variable exponents, specifically $3x$.
Step 2: To rewrite this expression, we use the power of a power rule for exponents, which states $(a^m)^n = a^{m \cdot n}$. In our case, we want to reverse this process: we express $10^{3x}$ as $(10^3)^x$. Here, by viewing $3x$ as the product of $3$ and $x$, we can apply the rule effectively.
Step 3: We now compare our converted expression $(10^3)^x$ with the provided answer choices. The correct rewritten form is:
- Choice 3: $\left(10^3\right)^x$
Therefore, the solution to the problem is $\left(10^3\right)^x$. This matches the correct answer provided, validating our analysis and application of the power of a power rule.