Final answer:
To simplify 1/x^-6, understanding negative exponents allows us to convert it to x^6, as negative exponents indicate inversion, moving the x term from the denominator to the numerator.
Step-by-step explanation:
To simplify the expression one over x raised to the negative sixth power, we must understand how negative exponents work.
Given the rule that a negative exponent denotes a division rather than multiplication, we can state that x-n is equivalent to 1/xn. Therefore, the expression 1/x-6 can be simplified into x6 because the negative exponent indicates that the x term should be moved to the numerator.
The rules for manipulating exponents, such as inverting the base when transitioning from a negative to a positive exponent or adding exponents when multiplying like bases, make simplifying expressions like these straightforward.