1. The problem asks to write the ratio $8w^2 : 6tw$ in the form $1 : n$ and express $n$ in terms of $t$ and $w$ in simplest form. 2. Recall that a ratio $a : b$ can be written as $1 : \frac{b}{a}$ by dividing both terms by $a$. 3. Apply this to the given ratio: $$1 : \frac{6tw}{8w^2}$$ 4. Simplify the fraction: $$\frac{6tw}{8w^2} = \frac{6t}{8w} = \frac{3t}{4w}$$ 5. Therefore, the ratio in the form $1 : n$ is: $$1 : \frac{3t}{4w}$$ 6. So the expression for $n$ in simplest form is: $$n = \frac{3t}{4w}$$