Rational Exponents

If n is a natural number greater than 1 and b is any real number, then equation

and since a negative exponent indicates a reciprocal, then equation

Example 1

Simplify each of the following.

  1. 36 1/2

  2. (72 x 4 y) 1/3

  3. 16 –(1/4)

  1. equation

  2. equation

  3. equation

If n is a natural number greater than 1, m is an integer, and b is a non‐negative real number, then equation

and equation

Example 2

Simplify each of the following.

  1. 27 2/3

  2. 25 –(3/2)

  1. equation

  2. equation