1. The problem is to simplify the expression $-3x^{-3}$. 2. Recall the rule for negative exponents: $x^{-n} = \frac{1}{x^n}$ for any positive integer $n$. 3. Apply this rule to rewrite $x^{-3}$ as $\frac{1}{x^3}$. 4. Thus, $-3x^{-3} = -3 \times \frac{1}{x^3} = \frac{-3}{x^3}$. 5. The expression simplified is $\frac{-3}{x^3}$.