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Negative Exponent Rule

Negative Exponent Rule

One-page printable reference

See It in Action

Two examples of the idea done right—and one common look-alike that is not right.

EXAMPLE

EXAMPLE

NON-EXAMPLE

Definition

The negative exponent rule states that for any nonzero number a and any integer n, the negative exponent a^-n is equivalent to the reciprocal of the base raised to the positive exponent. In other words:


a to the negative n power equals one over a to the n power.

Explanation:

  • If you have a base raised to a negative exponent, you move it to the denominator of a fraction and change the sign of the exponent to positive.

  • Conversely, if the base is in the denominator with a negative exponent, you move it to the numerator and change the sign of the exponent to positive.

Examples:

  1. Five to the negative three power equals one over five to the third power equals one over 125.
  2. X to the negative two power equals one over x squared.
  3. Two thirds to the negative four power equals three to the fourth power over two to the fourth power equals 81 over 16.

This rule helps simplify expressions involving negative exponents and makes them easier to work with.

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