The expression is \( \frac{50z^5}{10z^8} \). To simplify this:

1. Simplify the coefficients:
   \[
   \frac{50}{10} = 5
   \]

2. Subtract the exponents of \( z \) (since \( z^5 \) is in the numerator and \( z^8 \) is in the denominator):
   \[
   z^{5-8} = z^{-3}
   \]

So the simplified expression is:
\[
5z^{-3}
\]

This can also be written as:
\[
\frac{5}{z^3}
\]

Would you like further clarification or more details?

Here are some related questions:
1. How do you simplify expressions with negative exponents?
2. What are the laws of exponents?
3. How do you handle division with variables in expressions?
4. How can you rewrite expressions without negative exponents?
5. How do fractional exponents work in similar expressions?

**Tip:** When simplifying expressions, remember to handle the coefficients and variables separately, applying exponent rules to the variables.

Learn how to simplify the expression 50z^5 / 10z^8 step-by-step. This problem involves algebraic manipulation with exponents and division of polynomials. Suitable for students in Grades 7-9.

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