https://file.aiquickdraw.com/mathbot/file/1728529809802bza550fs.jpg

It looks like you've uploaded an image containing a mathematical expression. Based on the image, I can see the following terms:

\[
p^{-2} \cdot q^{-1} \cdot p^{11} \cdot q^{-6}
\]

We can simplify this expression by applying the rules of exponents:

1. Combine the exponents of like terms \( p \) and \( q \).

For \( p \), we add the exponents: 
\[
p^{-2} \cdot p^{11} = p^{-2 + 11} = p^9
\]

For \( q \), we add the exponents:
\[
q^{-1} \cdot q^{-6} = q^{-1 + (-6)} = q^{-7}
\]

So, the simplified expression is:
\[
p^9 \cdot q^{-7}
\]

Or, alternatively, it can be written as:
\[
\frac{p^9}{q^7}
\]

Would you like further details or explanations on any part of the process?

Here are some related questions to explore:
1. What are the rules of exponents and how do they work?
2. How can we simplify more complex expressions with exponents?
3. What happens if a base has a fractional exponent?
4. How do negative exponents relate to fractions?
5. Can you explain the difference between product and power rules for exponents?

**Tip:** Always remember, when multiplying terms with the same base, you simply add their exponents.

Simplify the expression: p^(-2) * q^(-1) * p^(11) * q^(-6)

This page explains how to simplify an expression involving exponents: p^(-2) * q^(-1) * p^(11) * q^(-6). Learn to apply the product of powers rule and negative exponents to get the final result: p^9 / q^7. Perfect for students in Grades 8-10.

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