1. **State the problem:** Simplify the expression $x^3 \cdot x^4$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents. 3. **Apply the rule:** $$x^3 \cdot x^4 = x^{3+4}$$ 4. **Simplify the exponent:** $$x^{3+4} = x^7$$ 5. **Final answer:** $$x^3 \cdot x^4 = x^7$$ This means when you multiply powers of the same base, you keep the base and add the exponents.