The expression given in the image is:

$\frac{2a^2b^7}{12a^3b^4}$

Simplifying Step-by-Step:

1. Simplify the coefficients: $\frac{2}{12} = \frac{1}{6}$

2. Simplify the powers of $a$: $\frac{a^2}{a^3} = a^{2-3} = a^{-1} = \frac{1}{a}$

3. Simplify the powers of $b$: $\frac{b^7}{b^4} = b^{7-4} = b^3$

Final Simplified Expression:

$\frac{b^3}{6a}$

This is the fully simplified version of the given expression.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might find helpful:

1. How would you simplify $\frac{3x^5y^2}{9x^2y^5}$?
2. What happens when the exponents are negative in similar expressions?
3. How can you simplify expressions involving roots instead of exponents?
4. How do you handle expressions with more than two variables?
5. What rules apply when both the base and exponent are fractions?

Tip: When dividing exponents with the same base, always subtract the exponents.