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To simplify the given expression \(\frac{x^{-5}}{x^{-3}}\), you apply the quotient rule for exponents. The rule states:

\[
\frac{x^a}{x^b} = x^{a-b}
\]

Here, \(a = -5\) and \(b = -3\). Applying the rule:

\[
\frac{x^{-5}}{x^{-3}} = x^{-5 - (-3)} = x^{-5 + 3} = x^{-2}
\]

Thus, the simplified expression is \(x^{-2}\), which corresponds to option **a: \(\frac{1}{x^2}\)**.

Would you like further details on this solution or have any other questions?

Here are 5 related questions to explore further:
1. How would you simplify \(\frac{x^7}{x^2}\)?
2. What is the general rule for negative exponents?
3. How does multiplying powers of the same base work?
4. How do you simplify an expression like \((x^{-3})^2\)?
5. What happens when you divide numbers with exponents but different bases?

**Tip:** When subtracting exponents in a fraction, always remember to account for negative signs properly!

Learn how to simplify the expression \(\frac{x^{-5}}{x^{-3}}\) using exponent rules. This problem involves subtracting exponents and applying the negative exponent rule. Suitable for students in Grades 8-10.

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