# Raising a Product or Quotient to a Power

It is important to know some general rules about exponents:

In radical notation, these properties are written as

####
**Exponent Rule #1**

*Whenever you multiply terms of the same base, you can add the exponents.*

**( x ^{m} ) ( x ^{n} ) = x^{( m + n )}**

**Note:** You ** cannot ** add the exponents in this case: (

*x*

^{4})(

*y*

^{3})

**because x and y are different base terms.**

Practice:

- Simplify
- Simplify

**Exponent Rule #2**

Whenever you have an exponent expression that is raised to a power, you can multiply the exponent and power:

**( x^{m} ) ^{n} = x ^{m n}**

Practice:

- Simplify
- Simplify
- Simplify (Note the "squared" applies to both x and y).

**Exponent Rule #3**

Anything to the power of zero is one.

**Exponent Rule #4**

If you are dividing quantities with the same base term, you can subtract the exponents.

Practice:

**Exponent Rule #5**

Practice:

These are the basic rules, although there are many more laws of exponents that stem from these.