The expression \( x^8 \cdot x^{-1} \) can be simplified using the rule of exponents:

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

In this case, \( a = 8 \) and \( b = -1 \), so we add the exponents:

\[
x^8 \cdot x^{-1} = x^{8 + (-1)} = x^7
\]

Thus, the simplified expression is:

\[
x^7
\]

Would you like further details on this or any related questions?

Here are 5 related questions you might want to explore:
1. How do you simplify \( x^a \cdot x^b \) when \( a \) and \( b \) are negative?
2. What happens when you multiply variables with different bases but the same exponents?
3. How do you divide powers with the same base, like \( x^a / x^b \)?
4. What is the result of raising a power to another power, like \( (x^a)^b \)?
5. How do you simplify expressions with fractional exponents?

**Tip:** Remember that multiplying powers of the same base is as simple as adding their exponents.

The query submitted by the user: x^8 * x^-1

Explore how to simplify the expression x^8 * x^-1 using exponent rules. This detailed solution demonstrates the application of exponentiation properties and the formula for multiplying powers with the same base. Ideal for students in Grades 6-8.

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