I have examined the image. Let's work through the simplifications step by step for each fraction:

1. $\frac{12a}{3}$: Simplify the coefficients:
   $\frac{12a}{3} = 4a$

2. $\frac{14ab^2}{2b}$: Simplify the coefficients and cancel common factors of $b$: $\frac{14ab^2}{2b} = \frac{14}{2} \cdot a \cdot \frac{b^2}{b} = 7ab$

3. $\frac{20b}{5b}$: The $b$'s cancel out, and simplify the coefficients: $\frac{20b}{5b} = 4$

4. $\frac{50b^2c^2}{5bc}$: Simplify the coefficients and cancel common factors of $b$ and $c$: $\frac{50b^2c^2}{5bc} = \frac{50}{5} \cdot \frac{b^2}{b} \cdot \frac{c^2}{c} = 10bc$

5. $\frac{35c^2}{7c}$: Simplify the coefficients and cancel a factor of $c$: $\frac{35c^2}{7c} = 5c$

6. $\frac{80ab^2c^3}{8b^2c^2}$: Simplify the coefficients and cancel common factors of $b$ and $c$: $\frac{80ab^2c^3}{8b^2c^2} = \frac{80}{8} \cdot \frac{b^2}{b^2} \cdot \frac{c^3}{c^2} = 10ac$

Let me know if you'd like further details or have any questions.

Related questions:

1. How can you simplify complex algebraic fractions more efficiently?
2. What is the importance of canceling common factors in algebra?
3. Can this method be applied to more complex polynomials?
4. What are the properties of exponents used in simplification?
5. How do you handle negative exponents in fraction simplification?

Tip: Always cancel out common factors carefully to avoid errors in simplification.