1. **State the problem:** Simplify the expression $$\frac{X^{-4} \cdot X^{3}}{X}$$. 2. **Recall the laws of exponents:** - When multiplying powers with the same base, add the exponents: $$a^{m} \cdot a^{n} = a^{m+n}$$. - When dividing powers with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. 3. **Apply the multiplication rule to the numerator:** $$X^{-4} \cdot X^{3} = X^{-4+3} = X^{-1}$$ 4. **Rewrite the original expression with the simplified numerator:** $$\frac{X^{-1}}{X}$$ 5. **Apply the division rule:** $$X^{-1} \div X^{1} = X^{-1-1} = X^{-2}$$ 6. **Final simplified form:** $$X^{-2} = \frac{1}{X^{2}}$$ **Answer:** The expression simplifies to $$\frac{1}{X^{2}}$$, which corresponds to choice C.