If \(x\) has a negative exponent, how is it expressed?

When a variable (x) has a negative exponent, it signifies that it can be expressed in terms of its reciprocal. Specifically, for a negative exponent (-n), the expression (x^{-n}) is equivalent to (1/x^{n}). This is the fundamental property of exponents that defines how negative exponents work.

For instance, if you have (x^{-3}), it can be rewritten as (1/x^{3}). This conversion from negative to positive exponents by taking the reciprocal is essential for simplifying expressions that involve powers.

The other choices do not accurately reflect this property of negative exponents. The expression (x^{n}) represents a positive exponent, while (x^{0}) is always equal to 1, regardless of (x) (assuming (x) is not zero). The expression (x^{-n}) still retains the negative exponent and does not provide the required form of its expression. Thus, the most appropriate representation for a negative exponent is indeed (1/x^{n}).