To simplify the expression
\[ \frac{(a + 3b)^2}{(a + 3b)^{-6}}, \]
we can use the properties of exponents. According to the quotient rule of exponents, when you divide two expressions with the same base, you subtract the exponents:
\[ \frac{x^m}{x^n} = x^{m - n}. \]
In our case, we have \( (a + 3b)^2 \) in the numerator and \( (a + 3b)^{-6} \) in the denominator. We can rewrite the expression applying the quotient rule:
\[ \frac{(a + 3b)^2}{(a + 3b)^{-6}} = (a + 3b)^{2 - (-6)} = (a + 3b)^{2 + 6} = (a + 3b)^{8}. \]
Since we want to express the final answer with positive exponents, we arrive at:
\[ (a + 3b)^8. \]
Therefore, the simplified expression is
\[ \boxed{(a + 3b)^8}. \]