# Rational Exponents

Exponents are those mathematical terms which represent number of times any number is multiplied to itself. Number that is multiplied to itself, is called as base and number of times it is multiplied is called its power. Rational Exponents are case of exponents where power to which a number is raised has a fractional form. All operations that we used to perform on exponents with non - fractional powers are applicable to those also with fractional powers. This may need some calculations for simplifying the problem. Power of rational exponents can be described as the numerator of power is power to which a number is raised to and denominator is degree of root of that number.

Root of any number 'A' can be defined as degree to which Numbers on other side of equal sign must be raised to make them equal to 'A'.
When you add or subtract powers during multiplication or division of rational exponents, you just have to find common denominator or degree of root to add or subtract numerators. It is similar to taking LCM (least common factor) of two numbers. Simplification of an expression can be done by leaving top term as power of expression, and put bottom term denoting the degree of root to the left of number. When you take reciprocal of a number raised to a negative rational exponent then exponent becomes positive. Addition and subtraction operations can only be performed if base and power of rational exponents are same. Only their coefficients are added or subtracted. Say for any two exponents: ab / c and aw / c,
ab/c + ab/c = 2 ab/c,
2ab/c – ab/c = ab/c,
ab/c * aw/c = ab/c + w/c = a (b + w)/c,
ab/c / aw/c = ab/c – w/c = a (b – w)/c.

## Properties of Rational Exponents

Rational numbers are number, which are in the form of p /q. 'p' and 'q' are two Real Numbers or whole numbers.
Rational exponents are in form of a p/q. Here 'a' is a real number, 'p' and 'q' are two real numbers, p/q is the rational exponent. Now we will see properties of Rational Exponents.
Property 1: If rational exponent is in form of ap/q then we c...Read More