Rational exponents

Raising a number to a power is reversed by finding the root of a number. We indicate roots by using rational exponents or radicals. In this sub-unit we will review definitions and rules concerning rational exponents.

Rational exponents are exponents of numbers that are expressed as a rational number,

A negative rational exponent indicates reciprocal just as a negative integral exponent does.

The rules of integer exponents also hold true for the rational powers as well.

Rules for Rational Exponents

The following rules are valid for all real numbers a and b and rational numbers  and  , provided that all indicated powers are real and no denominator is zero.

Negative exponents

We define negative power as the multiplicative inverse of the base raised to the positive opposite of the power.

A negative exponent is defined as the multiplicative inverse of the base raised to the power which is opposite to the given power.