Exponents – Definitions of Terms

Exponent: The power a number or variable is raised to in an expression.  This power can be positive, negative, zero, and fractional. Indeed, the exponent can be any real number. If the exponent is 0, then the value reduces to 1; that is, \(\begin{align}x^0 = 1\end{align}\), for every non-zero real number x.  Other examples:

  • \(\begin{align}2^3 = 2 \times 2 \times 2 = 8\end{align}\)
  • \(\begin{align}2^{-3} = \frac{1}{2^3} = \frac{1}{8}\end{align}\)
  • \(\begin{align}2^\frac{1}{2} = \sqrt{2}\end{align}\)

Power: An exponent given to a number or variable showing how many times the number (variable) is included in a product. Example: 4² = 4·4 = 16. In this example, 4 is said to be “raised” to the power of 2.