Exponential expressions have the form x^a, where x is the base and a is the exponent. x^a refers to the product,

where there are 'a' factors of the term x. For example,

The exponential expression x⁰ is equal to 1 for all x that are not equal to 0. When 0 is raised to an exponent of 0 (0⁰), the expression is undefined.

Exponents can take on different values, such as negative integers and fractions. The following formulas show how to calculate these types of exponential expressions.

Note: In general,

is simply written as

. In the expression x^1/a, if a is even, then x cannot be negative or it will be undefined.

Examples

Laws of Exponents

The following laws must be followed when multiplying and dividing powers. Laws a) and b) only apply when the two powers have the same base. Laws c) and d) only apply when the two bases are raised to the same exponent.