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The given expression to simplify is:

\[
\frac{p^{-7}}{p^{-6}}
\]

To simplify this, you apply the quotient rule for exponents. The quotient rule states that for any base \(a\) and exponents \(m\) and \(n\):

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

Applying this rule to the given expression:

\[
\frac{p^{-7}}{p^{-6}} = p^{-7 - (-6)} = p^{-7 + 6} = p^{-1}
\]

Thus, the simplified expression is:

\[
p^{-1}
\]

Or, alternatively:

\[
\frac{1}{p}
\]

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you simplify an expression with different bases?
2. What is the general rule for negative exponents?
3. How do you simplify products of powers with the same base?
4. What happens if the exponents in the quotient rule are positive?
5. How can you rewrite \( p^{-2} \) in fraction form?

**Tip:** Always remember that a negative exponent means the reciprocal of the base raised to the positive exponent!

Learn how to simplify the expression \( \frac{p^{-7}}{p^{-6}} \) using the quotient rule for exponents. This problem focuses on algebraic concepts, specifically exponentiation and simplification, making it ideal for students in Grades 8-10.

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