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, $c^{-n} = \frac{1}{c^n}$.