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To simplify the expression \( c^3 \cdot c^{-7} \), you can use the rule of exponents that states:

\[
a^m \cdot a^n = a^{m+n}
\]

Here, \( a \) is \( c \), \( m \) is 3, and \( n \) is \(-7\). So, applying the rule:

\[
c^3 \cdot c^{-7} = c^{3 + (-7)} = c^{-4}
\]

The simplified expression is:

\[
c^{-4}
\]

This can also be written as:

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

Would you like more details or have any questions about this process? 

Here are 5 related questions:
1. How do you simplify \( c^2 \cdot c^5 \)?
2. What is the result of \( x^4 \cdot x^{-2} \)?
3. How would you express \( y^{-3} \cdot y^3 \)?
4. Can you simplify the expression \( a^7 \cdot a^{-3} \)?
5. What happens when you multiply \( m^2 \) by \( m^{-2} \)?

**Tip:** Remember that a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, \( c^{-n} = \frac{1}{c^n} \).

Learn how to simplify the algebraic expression c^3 · c^-7 by applying the exponent rules. This problem demonstrates the concept of combining like bases with exponents, making it ideal for students in Grades 6-8.

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