# Rational Exponents

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

is called the base, is called the exponent and is an exponential expression and is read as ' to the nth power' or ' to the nth'.

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.

Subsections

Department of Mathematics