Final answer:
The expression log(x)/z⁶ is already in its simplest form as log(x) * z⁻⁶. There are no further simplifications that can be made without additional context or operations.
Step-by-step explanation:
To expand the expression log(x)/z⁶ in terms of variables and simplify it, we need to recognize that logarithms can be manipulated using the laws of logarithms and that a term in the denominator with an exponent represents a negative exponent when moved to the numerator.
First, we note that the expression log(x)/z⁶ can be interpreted as log(x) * z⁻⁶. Then, by using the property of logarithms that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (Property 3), we could simplify an expression if x were to the power of z, but in this case, there is no such exponent to work with and the logarithm and the term z⁶ are separate.
Therefore, the expression is already as simple as it can be unless more context or additional operations are specified.