If a similar phrase appears in both the numerator and the denominator of the fraction and these similar phrases are connected at the highest level by multiplication, then the similar phrases may be canceled. A number of rewriting rules exist within algebra to simplify a with a shorthand notation. Exponential notation is an example of a shorthand notational scheme. If a series of similar algebraic phrases are multiplied times one another, the expression may be rewritten with the phrase raised to a power. The power is the number of times the phrase is multiplied by itself and is written as a superscript of the phrase.
Some special rules apply to exponents.
A negative exponent may be transformed to a positive exponent if the base is changed to one divided by the base. The following examples illustrate this principle. A special form of exponential notation, called binomial expansion occurs when a phrase connected with addition or subtraction operators is raised to the second power. 2 A more complex example of the preceding occurs when the phrase being squared has more than two terms. In its simplest form, if a number or variable is multiplied by a phrase connected at the highest level with the addition or subtraction operator, the phrase may be rewritten as the variable or number times each term in the phrase.