What Is Rational Exponent Notation?

Standard Exponent Notation

• The number that is being multiplied by itself is called the "base" number; base numbers are written just like any other regular number in an equation. The number of times the base number multiplied by itself is called the "exponent." An exponent appears above and to the right the base number, often smaller and, when in print, in italics. A rational exponent is when both the base number and exponent and positive integers; any exponential number written such that both terms are expressed as positive integers is in rational exponent notation.

Fractional Exponents

• Fractional exponents occur when a base number has an exponent that is represented as a fraction; this represents the number of times the base number will be divided (not multiplied) by itself. Any number "x" to the 1/2 power is therefore equal to the square root of x. For example, 36 to the 1/2 power equals 6. Similarly, x to the 1/3 is equal to the cubed root of x; 125 to the 1/3 power equals 5.

Root Notation

• Root notation is in many ways the opposite of rational exponent notation. Roots are written with the radical symbol, which looks like a large check mark. The number inside the radical symbol is the base, and the exponent is on the outside of the radical symbol, appearing above and to the left of the base; the exponent in this case indicates the number of times the base will be divided by itself.

Order of Operations

• The order of mathematical operations dictates that exponents are solved second after parenthetical computations. After solving for both the parenthetical and exponential parts of the equation, you move onto any multiplication, division, addition and subtraction elements of the equation, in that order.