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The given expression is:

\[
\frac{z^{-5}}{z^{-1}}
\]

To simplify this expression using only positive exponents, apply the law of exponents: 

\[
\frac{a^m}{a^n} = a^{m-n}
\]

In this case, we have:

\[
z^{-5} \div z^{-1} = z^{-5 - (-1)} = z^{-5 + 1} = z^{-4}
\]

Now, express this with positive exponents:

\[
z^{-4} = \frac{1}{z^4}
\]

So, the simplified expression with only positive exponents is:

\[
\frac{1}{z^4}
\]

Would you like more details or have any further questions?

Here are 5 related questions you might find interesting:
1. How do you simplify \(\frac{x^{-3}}{x^{-6}}\)?
2. What is the result of simplifying \(\frac{y^2}{y^{-4}}\)?
3. How would you simplify \(\frac{a^{-2}b^3}{a^{-4}b^{-1}}\)?
4. What happens when you simplify \(\left(\frac{x^3}{y^{-2}}\right)^2\)?
5. Can you simplify \(\frac{1}{z^{-2}}\)?

**Tip**: When simplifying expressions with exponents, always remember that subtracting exponents is equivalent to division and adding them is equivalent to multiplication.

Step-by-step guide on simplifying expressions using negative exponents. Learn how to use the laws of exponents effectively to solve problems like z^{-5} / z^{-1} and convert them to expressions with only positive exponents.

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