Simplify the Expression: 7^(x+a) × 7^a × 7^x

To solve this problem, we'll start by applying the rules for multiplying powers with the same base.

• Step 1: Identify the expression given as $7^{x+a} \times 7^a \times 7^x$.
• Step 2: Apply the rule $a^m \times a^n = a^{m+n}$ to combine the exponents since all terms have the same base, 7.

Let's proceed to simplify:

Combine the exponents:

$7^{x+a} \times 7^a \times 7^x = 7^{(x+a) + a + x}$.

Now, simplify the addition of the exponents:

$7^{(x+a) + a + x} = 7^{x + a + a + x}$.

Combine like terms in the exponent:

$x + a + a + x = 2x + 2a$.

Thus, the expression simplifies to:

$7^{2x+2a}$.

Therefore, the simplification of the given expression is $7^{2x+2a}$.