The expression \( x^{-9} \cdot x^7 \) can be simplified using the rule of exponents:

\[
x^a \cdot x^b = x^{a+b}
\]

In this case, we have:

\[
x^{-9} \cdot x^7 = x^{-9 + 7} = x^{-2}
\]

Thus, the simplified expression is:

\[
x^{-2} = \frac{1}{x^2}
\]

Would you like any further explanation or details on exponent rules?

Here are 5 related questions to explore further:
1. How do you simplify \( x^a \cdot x^b \) when \( a \) and \( b \) are different?
2. What happens when you divide powers with the same base?
3. How do you deal with negative exponents in other contexts?
4. What is the general rule for \( (x^a)^b \)?
5. How would you simplify \( \frac{x^7}{x^9} \)?

**Tip**: Remember, a negative exponent means you take the reciprocal of the base raised to the positive exponent.

Simplify the expression x^-9 · x^7 using exponent rules. This solution demonstrates how to add exponents with the same base and provides insight into handling negative exponents. Suitable for students in Grades 8-10.

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