$F(x, y)$ is homogeneous of degree $n$, $F(1, 2) = 3$ and $F(3, 6) = 243$. What is $n$?

Explanation

1. 01

   $(3, 6) = (3 \cdot 1, 3 \cdot 2)$, so $F(3, 6) = 3^{n}F(1, 2)$: $3^{n} \cdot 3 = 243$.

2. 02

   $3^{n} = 81 = 3^{4}$, so $n = 4$.