1. Properties of Exponents

2. To multiply terms with the same base, add the exponents.
Product of Powers
To multiply terms with the same base, add the exponents.
Example:
73 x 78 = 73+8 = 711

3. To divide terms with the same base, subtract the exponents.
Quotient of Powers
To divide terms with the same base, subtract the exponents.
Example:
108
= = 105
103

4. To raise a power to a power, multiply the exponents.
Power of Powers
To raise a power to a power, multiply the exponents.
Example:
(52)6 = 52x6 = 512

5. Power of a Product Example:
To multiply terms with different bases raised to the same power, multiply first and raise the product to the given power.
Example:
23 x 33 = (2 x 3)3 = 63

6. ( ) Power of a Quotient = = Example:
To divide terms with different bases raised to the same power, raise both numerator and denominator to the power.
Example:
( ) 4 16 2 42 = = 92 81 9

7. Raising a base (other than zero) to the zero power equals one.
Zero Exponents
Raising a base (other than zero) to the zero power equals one.
Example:
1000 = 1

8. Negative Exponents Example:
Raising a base to a negative power equals the reciprocal of the base raised to the absolute value of the power.
Example: 1
4-9 = 49