1. **State the problem:** Simplify the expression $$\frac{2x^4 y^3}{-9x^3 y^7}$$ and write the result using positive exponents. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Negative signs can be factored out. - Keep exponents positive by rewriting negative exponents as reciprocals. 3. **Apply the rules to the expression:** $$\frac{2x^4 y^3}{-9x^3 y^7} = \frac{2}{-9} \times \frac{x^4}{x^3} \times \frac{y^3}{y^7}$$ 4. **Simplify each part:** - Coefficients: $$\frac{2}{-9} = -\frac{2}{9}$$ - For $$x$$: $$x^{4-3} = x^1 = x$$ - For $$y$$: $$y^{3-7} = y^{-4}$$ 5. **Rewrite with positive exponents:** $$y^{-4} = \frac{1}{y^4}$$ 6. **Combine all parts:** $$-\frac{2}{9} \times x \times \frac{1}{y^4} = -\frac{2x}{9y^4}$$ **Final answer:** $$\boxed{-\frac{2x}{9y^4}}$$