Complete the Expression: (11/19) Raised to (a+3b) Power

Insert the corresponding expression:

$\left(\frac{11}{19}\right)^{a+3b}=$

To solve this problem, we need to rewrite the expression $\left(\frac{11}{19}\right)^{a+3b}$ using the rules for powers of fractions. Specifically, we apply the exponent to both the numerator and the denominator separately.

According to the rule $\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$, we apply the exponent $a+3b$ to both 11 and 19:

$\left(\frac{11}{19}\right)^{a+3b} = \frac{11^{a+3b}}{19^{a+3b}}$

Therefore, the expression can be rewritten as $\frac{11^{a+3b}}{19^{a+3b}}$, matching choice 3 in the provided options.

Hence, the solution to the problem is $\frac{11^{a+3b}}{19^{a+3b}}$.