To simplify the expression $\frac{x^6}{x^8}$ and rewrite it in the form $x^n$:

We can use the rule of exponents which states:

$\frac{x^a}{x^b} = x^{a-b}$

Here, $a = 6$ and $b = 8$. Therefore:

$\frac{x^6}{x^8} = x^{6-8} = x^{-2}$

So the simplified expression is $x^{-2}$.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. What is the simplified form of $\frac{x^3}{x^7}$?
2. How would you simplify $\frac{x^{10}}{x^4}$?
3. What is the rule for multiplying exponents, such as $x^2 \times x^3$?
4. Can you simplify $\frac{y^5 \cdot x^3}{y^2 \cdot x^4}$?
5. What does a negative exponent signify in terms of fractions?

Tip: Remember that a negative exponent means you can express it as a reciprocal. For example, $x^{-2} = \frac{1}{x^2}$.