1. **State the problem:** Simplify the expression $$\frac{(2u^{2}v^{3}w^{3})(5u^{3}v^{4}w^{2})}{\frac{-2x^{3}y^{2}z}{6x^{2}y^{3}z^{6}}} \quad \text{and} \quad \frac{(3s^{11})(9s^{-5})}{\frac{25p^{5}qr^{2}}{5p^{2}qr}}$$ 2. **Recall the rules:** - Multiply powers with the same base by adding exponents: $a^{m} \times a^{n} = a^{m+n}$. - Divide powers with the same base by subtracting exponents: $\frac{a^{m}}{a^{n}} = a^{m-n}$. - When dividing fractions, multiply by the reciprocal. --- ### Left fraction: 3. Multiply the numerators: $$ (2u^{2}v^{3}w^{3})(5u^{3}v^{4}w^{2}) = 2 \times 5 \times u^{2+3} \times v^{3+4} \times w^{3+2} = 10u^{5}v^{7}w^{5} $$ 4. Simplify the denominator fraction: $$ \frac{-2x^{3}y^{2}z}{6x^{2}y^{3}z^{6}} = -\frac{2}{6} \times x^{3-2} \times y^{2-3} \times z^{1-6} = -\frac{1}{3} x^{1} y^{-1} z^{-5} = -\frac{1}{3} x y^{-1} z^{-5} $$ 5. Dividing by a fraction is multiplying by its reciprocal: $$ \frac{10u^{5}v^{7}w^{5}}{-\frac{1}{3} x y^{-1} z^{-5}} = 10u^{5}v^{7}w^{5} \times \left(-3 \frac{1}{x y^{-1} z^{-5}}\right) = -30 u^{5} v^{7} w^{5} \times \frac{1}{x y^{-1} z^{-5}} $$ 6. Simplify the denominator inside the reciprocal: $$ \frac{1}{x y^{-1} z^{-5}} = x^{-1} y^{1} z^{5} $$ 7. Multiply all terms: $$ -30 u^{5} v^{7} w^{5} x^{-1} y^{1} z^{5} = -30 u^{5} v^{7} w^{5} y x^{-1} z^{5} $$ --- ### Right fraction: 8. Multiply the numerators: $$ (3s^{11})(9s^{-5}) = 3 \times 9 \times s^{11 + (-5)} = 27 s^{6} $$ 9. Simplify the denominator fraction: $$ \frac{25 p^{5} q r^{2}}{5 p^{2} q r} = \frac{25}{5} \times p^{5-2} \times q^{1-1} \times r^{2-1} = 5 p^{3} r^{1} = 5 p^{3} r $$ 10. Divide numerator by denominator: $$ \frac{27 s^{6}}{5 p^{3} r} = \frac{27}{5} s^{6} p^{-3} r^{-1} $$ --- **Final answers:** $$ \boxed{\text{Left fraction} = -30 u^{5} v^{7} w^{5} y x^{-1} z^{5}} $$ $$ \boxed{\text{Right fraction} = \frac{27}{5} s^{6} p^{-3} r^{-1}} $$