Properties of Exponents

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

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 = 108-3 = 105 103

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

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

( ) 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

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

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