Simplify the Expression: 7^(x+1) × 7^x Using Exponent Rules

To solve the problem $7^{x+1}\times7^x$, follow these steps:

Step 1: Use the rule for multiplying powers with the same base:

$a^m \cdot a^n = a^{m+n}$

Here, the base $a$ is $7$, and the exponents are $x+1$ and $x$.

Step 2: Add the exponents:

The expression becomes $7^{(x+1) + x}$.

Step 3: Simplify the exponents:

$(x+1) + x = 2x + 1$

Step 4: Write the final expression:

The simplified expression is $7^{2x+1}$.

Therefore, our solution matches choice 3.

The solution to the problem is $7^{2x+1}$.