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The given expression is:

\[
\frac{x^{-6}}{x^{-2}}
\]

To simplify, use the rule of exponents:

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

In this case, \( a = x \), \( m = -6 \), and \( n = -2 \). So,

\[
\frac{x^{-6}}{x^{-2}} = x^{-6 - (-2)} = x^{-6 + 2} = x^{-4}
\]

To express the answer with a positive exponent, we rewrite \( x^{-4} \) as:

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

Thus, the simplified expression is:

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

Would you like further details or have any questions?

Here are some related questions to practice:

1. Simplify: \(\frac{y^{-3}}{y^{-5}}\)
2. Simplify: \(\frac{z^{-8}}{z^{-3}}\)
3. Simplify: \(\frac{a^5}{a^2}\)
4. Simplify: \(\frac{b^0}{b^{-4}}\)
5. Simplify: \(\frac{w^{-7}}{w^2}\)

**Tip:** When simplifying exponents, remember that dividing powers with the same base means subtracting the exponents.

Simplify \( \frac{x^{-6}}{x^{-2}} \) and write the answer with a positive exponent only.

Learn how to simplify \( \frac{x^{-6}}{x^{-2}} \) by applying the exponent rules. This detailed guide demonstrates key algebraic principles and explains how to express answers with positive exponents. Suitable for students in Grades 8-10.

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