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# Exponent Rules

## 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:
an
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:
Can + Dan = (C + D)an

Example:
2x3 + 3x3 = 5(x3)

### 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:
Can – Dan = (C – D)an

Example:
6x3 – 3x3 = 3(x3)

### Exponent Multiplication Rule

We can multiply exponent terms as long as they have the same base a. The rule is given as:
(an)(am) = a(n + m)

Example:
(52)(54) = 56

### Exponent Division Rule

We can divide exponent terms as long as they have the same base a. The rule is given as:
(an)/(am) = a(n – m)

Example:
(55)/(52) = 53

### Exponent Power Rule

We can raise an exponent term to a power. The rule is given as:
(an)m = a(n·m)

Example:
(x3)4 = x12

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