What is involved in simplifying an expression with a negative power?

When simplifying an expression with a negative power, the process involves transforming the expression into a more manageable form. A negative exponent indicates that the base should be moved to the denominator of a fraction and converted into a positive power. This is a fundamental property of exponents.

For instance, if you have a term like ( x^{-n} ), it can be rewritten as ( \frac{1}{x^n} ). This is akin to "multiplying by the base to the positive power," which, in fractional notation, effectively means you are recognizing that a negative exponent represents a reciprocal relationship. Therefore, multiplying by the base to the positive power aligns perfectly with the rule governing negative exponents, making it the correct approach to simplification.

The other options do not accurately represent the rules about negative exponents:

• Dividing the base by one does not change the base's power and does not yield a simplification.
• Adding 1 to the exponent is not valid for dealing with negative exponents, as it does not follow exponentiation rules.
• Changing the base to zero is incorrect, as an expression with a base of zero and a negative exponent is undefined.

Thus, understanding that a negative exponent signals a reciprocal relationship with