We need to simplify the expression $(\frac{n^3}{-4})^3$.

1. Problem Description

We need to simplify the expression $(\frac{n^3}{-4})^3$.

2. Solution Steps

First, we need to apply the power of a quotient rule, which states that $(\frac{a}{b})^c = \frac{a^c}{b^c}$.

Applying this rule to our expression, we have:

$(\frac{n^3}{-4})^3 = \frac{(n^3)^3}{(-4)^3}$

Next, we apply the power of a power rule, which states that $(a^b)^c = a^{b \cdot c}$.

$(n^3)^3 = n^{3 \cdot 3} = n^9$

Then, we evaluate $(-4)^3$:

$(-4)^3 = (-4) \cdot (-4) \cdot (-4) = 16 \cdot (-4) = -64$

Substituting these results back into our expression, we get:

$\frac{n^9}{-64}$

Therefore, the simplified expression is $-\frac{n^9}{64}$.

3. Final Answer

$-\frac{n^9}{64}$