1. The problem involves applying the laws of exponents to simplify expressions. 2. Recall the key exponent rules: - Product rule: $$a^m \times a^n = a^{m+n}$$ - Quotient rule: $$\frac{a^m}{a^n} = a^{m-n}$$ - Power rule: $$(a^m)^n = a^{mn}$$ - Zero exponent: $$a^0 = 1$$ (for $a \neq 0$) 3. For the expression $$25x^7 \div (-5x^2)$$, first divide the coefficients: $$\frac{25}{-5} = \cancel{\frac{25}{-5}} = -5$$ 4. Then apply the quotient rule for the variables: $$x^{7-2} = x^5$$ 5. Combine the results: $$-5x^5$$ 6. For the expression $$-5x$$, it is already simplified. 7. The answers for the given problems are: - #1: $$-5x^5$$ - #2: $$-5x$$ This completes the simplification using the laws of exponents.