**Positive Exponents:** If is a real number and is a natural number, **the nth power of **:

**Negative Exponents:** For all real numbers , and all natural numbers , for which is a real number

**th Root:** If is a real number, and is a natural number for which

is **the th root of **, that is

if
either and is an even positive integer

or is odd positive integer

**Rational Exponents:**
For all real number , and all positive integers and for which is a real number

**Rules for Exponents** For all integers and and all real numbers and :

1.

2.

3.

4.
,

5.

6.
,

7. ,

__Remark__ The above rules hold when and are rational numbers and and are positive real numbers.

Department of Mathematics