1. **Stating the problem:** Simplify or express the given expression $x^{-3} y^{4}$. 2. **Recall the rules:** - Negative exponents mean reciprocal: $a^{-n} = \frac{1}{a^n}$. - Positive exponents mean repeated multiplication. 3. **Apply the negative exponent rule:** $$x^{-3} y^{4} = \frac{y^{4}}{x^{3}}$$ 4. **Final expression:** The expression $x^{-3} y^{4}$ can be rewritten as $$\frac{y^{4}}{x^{3}}$$ which is often easier to interpret or use in further calculations. This is the simplified form of the given expression.