RATIONAL EXPONENTS

EXPONENT OF THE FORM

Example

TO CONVERT FROM EXPONENT FORM TO RADICAL FORM

and .

Please note that in the fractional exponent, the top(numerator) is the power
and the bottom (denominator) is the root.

Example 1.

Example 2.

NEGATIVE INTEGER EXPONENTS

Rule:

if x

Example

ODD AND EVEN POWERS

Since Multiplication of an odd number of negatives is negative and
since multiplication of an even number of negatives is positive,
we can say that a negative raised to an odd power is negative and
a negative raised to an even power is positive.
Given that r is an integer, if r is odd.

THE ELEVATOR RULE

  1. Given :

Example:

2. Given :

Example:


THE ELEVATOR RULE APPLIES ONLY TO FACTORS WITH NEGATIVE

EXPONENTS.

Example rational exponents:

1.