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# Exponent Rules

#### Lesson Contents

## The Five Categories of Exponent Rules

**Terms that have exponents can be added, subtracted, multiplied, divided, and raised to a power.** There is an exponent rule for each of these elementary math operations.

A term with an exponent is generally notated as:

**a ^{n}**

Where *a* is the base and *n* is the exponent. This is the form of writing an exponent term that we will use throughout the lesson and for the exponent rule formulas.

### Exponent Addition Rule

**We can add exponent terms as long as they have the same base a and exponent n.** The rule is given as:

**Ca ^{n} + Da^{n} = (C + D)a^{n}**

Example:

2x^{3} + 3x^{3} = 5(x^{3})

### Exponent Subtraction Rule

**We can subtract exponent terms as long as they have the same base a and exponent n.** The rule is given as:

**Ca ^{n} – Da^{n} = (C – D)a^{n}**

Example:

6x^{3} – 3x^{3} = 3(x^{3})

### Exponent Multiplication Rule

**We can multiply exponent terms as long as they have the same base a.** The rule is given as:

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

Example:

(5^{2})(5^{4}) = 5^{6}

### Exponent Division Rule

**We can divide exponent terms as long as they have the same base a.** The rule is given as:

**(a ^{n})/(a^{m}) = a^{(n – m)}**

Example:

(5^{5})/(5^{2}) = 5^{3}

### Exponent Power Rule

**We can raise an exponent term to a power.** The rule is given as:

**(a ^{n})^{m} = a^{(n·m)}**

Example:

(x^{3})^{4} = x^{12}