1. **State the problem:** Simplify the expression $$\frac{18 \cdot 7a^5 b^6 c}{14a^5 b^9}$$. 2. **Write the expression clearly:** $$\frac{18 \times 7a^5 b^6 c}{14a^5 b^9}$$ 3. **Multiply constants in numerator:** $$18 \times 7 = 126$$ So the expression becomes: $$\frac{126 a^5 b^6 c}{14 a^5 b^9}$$ 4. **Simplify the fraction of constants:** $$\frac{126}{14} = \frac{\cancel{126}^{9} \times 14}{\cancel{14} \times 1} = 9$$ 5. **Cancel common factors in variables:** - For $a^5$ in numerator and denominator: $$\frac{a^5}{a^5} = 1$$ - For $b^6$ and $b^9$: $$\frac{b^6}{b^9} = \frac{\cancel{b^6}^1}{b^{\cancel{6}^3}} = \frac{1}{b^3}$$ 6. **Rewrite the simplified expression:** $$9 \times c \times \frac{1}{b^3} = \frac{9c}{b^3}$$ **Final answer:** $$\boxed{\frac{9c}{b^3}}$$