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I can see that you've uploaded two mathematical expressions for simplification. Let's solve each one:

### Problem 2: 
\[
\frac{5z^5 w^4}{9z w^2}
\]
1. Simplify the powers of \(z\): \(z^5 / z = z^{5-1} = z^4\).
2. Simplify the powers of \(w\): \(w^4 / w^2 = w^{4-2} = w^2\).

So the simplified expression is:
\[
\frac{5z^4 w^2}{9}
\]

### Problem 3:
\[
\frac{gy}{4g^6 y^4}
\]
1. Simplify the powers of \(g\): \(g / g^6 = g^{1-6} = g^{-5}\).
2. Simplify the powers of \(y\): \(y / y^4 = y^{1-4} = y^{-3}\).

So the simplified expression is:
\[
\frac{g^{-5} y^{-3}}{4} = \frac{1}{4g^5 y^3}
\]

If you'd like further details or have any questions, feel free to ask!

Here are some related questions for practice:
1. How would you simplify \(\frac{a^3 b^5}{a^2 b^2}\)?
2. How do you simplify expressions with negative exponents?
3. Can you explain how to simplify fractional exponents?
4. What happens when you have \(x^0\) in a fraction?
5. How can we factor polynomials with exponents?

**Tip:** Always remember the rule of subtracting exponents when dividing powers with the same base!

Simplify the following algebraic fractions:
2) \(\frac{5z^5 w^4}{9z w^2}\)
3) \(\frac{gy}{4g^6 y^4}\)

Learn how to simplify algebraic fractions involving exponents with detailed solutions. Problems include expressions with variables like z, w, g, and y, using exponent rules to simplify. Suitable for students in Grades 8-10.

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