To simplify the expression \(c^n \times c^{-q} + c^{-2}\), we can use the laws of exponents. Let's go through the steps.

### Step 1: Simplify \(c^n \times c^{-q}\)

Using the exponent rule that states \(a^m \times a^n = a^{m+n}\), we can combine the exponents:

\[
c^n \times c^{-q} = c^{n + (-q)} = c^{n - q}
\]

### Step 2: Combine with the remaining term

Now, substitute this back into the original expression:

\[
c^{n - q} + c^{-2}
\]

This is the simplified form of the expression. Since there are no like terms or common factors that can be further simplified, this is as simplified as it gets.

**Final Simplified Expression:**
\[
c^{n - q} + c^{-2}
\]

Would you like further details or have any questions?

### Related Questions:

1. What are the rules for multiplying and dividing powers with the same base?
2. How do you simplify expressions with negative exponents?
3. What are the different ways to handle expressions that involve exponents?
4. How do you expand expressions involving powers with different bases?
5. How can you express a term with a negative exponent as a fraction?

### Tip:
When dealing with exponents, remember that negative exponents represent reciprocal values, so \(a^{-n} = \frac{1}{a^n}\).

Learn how to simplify the expression c^n × c^-q + c^-2 using the laws of exponents. This problem covers key concepts in exponents and their applications. Suitable for students in Grades 7-9.

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