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We are asked to simplify \( q^0 \cdot q^9 \).

Let's break this down:

1. \( q^0 = 1 \) because any number raised to the power of 0 equals 1, except when the base is zero.
2. Therefore, the expression becomes:
   \[
   q^0 \cdot q^9 = 1 \cdot q^9 = q^9
   \]

The simplified expression is \( q^9 \).

Do you have any questions or want further details on this solution?

Here are some related questions to explore:

1. What happens if \( q \) is equal to 0 in the original expression?
2. How do we simplify \( q^m \cdot q^n \) in general?
3. What is the result of \( q^0 + q^9 \), and how does it differ from multiplication?
4. How would you simplify \( q^{-2} \cdot q^4 \)?
5. What would happen if the bases were different, like \( q^0 \cdot r^9 \)?

**Tip**: Always remember that any non-zero base raised to the power of 0 equals 1.

Simplify. Express your answer as a single term, without a denominator: q^0 * q^9

Learn how to simplify the expression q^0 * q^9 using exponent rules. This problem introduces key concepts such as the zero exponent rule and multiplying powers with the same base. Suitable for students in Grades 6-8.

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