1. **State the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Recall the laws of exponents:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ - Constants can be divided normally. 3. **Divide the constants:** $$\frac{25}{-5} = -5$$ 4. **Apply the exponent rule to the variable:** $$\frac{x^7}{x^2} = x^{7-2} = x^5$$ 5. **Combine the results:** $$-5 \times x^5 = -5x^5$$ 6. **Show intermediate cancellation:** $$\frac{\cancel{25}x^7}{\cancel{-5}x^2} = -5x^{7-2} = -5x^5$$ 7. **Final answer:** $$\boxed{-5x^5}$$