Final answer:
To simplify the expression x to the -6 / x to the power of 8, apply the rules for negative exponents and subtract exponents when dividing with the same base to get 1 / x to the 14th power.
Step-by-step explanation:
To simplify the expression x to the -6 / x to the power of 8, we need to use the rules of exponents. Specifically, we'll use the rules for negative exponents and for dividing with the same base. The rule for negative exponents states that a negative exponent denotes a division rather than multiplication, or in other words, flipping the construction to the denominator. That is, x-n = 1 / xn.
When dividing with the same base, we subtract the exponents. So for our expression x-6 / x8, this becomes x-6 - 8, which simplifies to x-14. Applying the rule for negative exponents, this becomes 1 / x14.