The given expression is:

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

We will simplify the expression by using the exponent rule for division:

$\frac{a^m}{a^n} = a^{m-n}$

For this problem:

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

Therefore, the simplified expression is:

$x^2$

Let me know if you need further details or have any questions. Here are some related questions you might find useful:

1. What is the power of a quotient rule for exponents?
2. How can negative exponents be written as fractions?
3. What is the rule for multiplying powers with the same base?
4. How do you simplify expressions with fractional exponents?
5. What happens when you divide expressions with exponents of the same base?

Tip: When simplifying exponents, remember that negative exponents indicate the reciprocal of the base raised to the positive exponent.