# Rules of Exponents

## Definitions

Terminology
We would call this “x raised to the a power” x is called the base
a is called the exponent

Example: is called “seven raised to the eleventh power”
the base is 7
the exponent is 11

Integer exponents
An integer exponent just means multiplying a number by itself. Example:  Fraction exponents
An exponent which is the reciprocal of an integer means taking the root Example:  Negative exponents
A negative exponent indicates a reciprocal Example:  NOTICE: This means you don’t ever have to deal with fractions or roots ever again if you don’t want to! You can treat them all like exponents.

## Algebra rules

Combining exponents
When two numbers with the same base are multiplied, the exponents may be added Example:  Exponents in ratios
When exponents in the numerator an denominator have the same base, their exponents may be subracted NOTE: This is just a combination of the negative exponent rule with the multiplication rule!

Distributing exponents
If you have 2 layers of exponents, they may be combined Example:  Negative bases
When the base is a negative number, the sign of the expression overall depends on whether the exponent is even or odd. if n is an odd integer if n is an even integer

Therefore: if n is an odd integer if n is an even integer

Examples:  Exponents DO NOT distribute cleanly over addition You either have to find a way to simplify the base first OR use the definition of the exponent to simplify things.
Examples:     