Solve (5/9)^(2x+1): Complete the Exponential Expression

To solve this problem, we'll apply the power of a fraction rule, which states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

Step 1: Recognize the given expression: $\left(\frac{5}{9}\right)^{2x+1}$.

Step 2: Apply the exponent rule to rewrite the expression. According to the rule, this becomes:

$\left(\frac{5}{9}\right)^{2x+1} = \frac{5^{2x+1}}{9^{2x+1}}$.

Therefore, the expression can be rewritten as $\frac{5^{2x+1}}{9^{2x+1}}$.

Among the given choices, the correct option is choice 1: $\frac{5^{2x+1}}{9^{2x+1}}$.

Thus, the solution to the problem is $\frac{5^{2x+1}}{9^{2x+1}}$.