1. **State the problem:** Simplify the expression $$\frac{-3x^6}{5x^3} \cdot 3x^3$$. 2. **Recall the rules:** - When multiplying fractions, multiply numerators and denominators separately. - When multiplying powers with the same base, add the exponents: $$x^a \cdot x^b = x^{a+b}$$. - When dividing powers with the same base, subtract the exponents: $$\frac{x^a}{x^b} = x^{a-b}$$. 3. **Rewrite the expression:** $$\frac{-3x^6}{5x^3} \cdot 3x^3 = \frac{-3x^6 \cdot 3x^3}{5x^3}$$ 4. **Multiply the numerators:** $$-3 \cdot 3 = -9$$ $$x^6 \cdot x^3 = x^{6+3} = x^9$$ So numerator is $$-9x^9$$. 5. **Write the fraction:** $$\frac{-9x^9}{5x^3}$$ 6. **Simplify the powers of $$x$$ by subtracting exponents:** $$\frac{-9\cancel{x^9}}{5\cancel{x^3}} = \frac{-9x^{9-3}}{5} = \frac{-9x^6}{5}$$ 7. **Final simplified expression:** $$-\frac{9}{5}x^6$$ This is the simplified form of the given expression.