1. **Stating the problem:** Simplify the expression $$\frac{25x^7}{-5x^2}$$ using the laws of exponents. 2. **Formula and rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Division of coefficients is done normally. - A negative sign in the denominator can be factored out as a negative sign in front. 3. **Step-by-step simplification:** - Divide the coefficients: $$\frac{25}{-5} = \cancel{\frac{25}{-5}} = -5$$. - Subtract the exponents of $x$: $$x^{7-2} = x^5$$. 4. **Combine results:** $$\frac{25x^7}{-5x^2} = -5x^5$$. 5. **Final answer:** $$\boxed{-5x^5}$$ This shows how to apply the laws of exponents to simplify expressions involving division of powers with the same base.