Exponents

6³ Exponent Base

6³ is read “Six Cubed” 6³ = 6 x 6 x 6 6³ = 216

Any base to the zero power, equals one. Example: Any base to the first power, equals itself. 50 = 1 20 = 1 41 = 4 71 = 7

Evaluate Exponents Evaluating Exponents: means to find the VALUE of. Example: 3² = -9º = (-3)³ =

Evaluate the following: = = = = 1 125 -9 3 100 64 1 16 -1 -7

Properties of Exponents Complete the table in your notes and look for a pattern

Rule 1: When multiplying two numbers with the same base, keep base and add the exponents. 3³ x 3² . x 3 x 3 x 3 x 3 x 3 3 x 3 x 3 3 x 3

Properties of Exponents Complete the table in your notes and look for a pattern

Rule 2: When dividing two numbers with the same base, keep base and subtract the exponents.

Rule 3 (3²) x (3²) x (3²) (3 x 3) x (3 x 3) x (3 x 3) When raising a number with an exponent to a power, multiply the exponents. (3²)³ (3²) x (3²) x (3²) (3 x 3) x (3 x 3) x (3 x 3) 3 x 3 x 3 x 3 x 3 x 3

Negative Exponents Negative Exponents are NOT negative numbers Negative Exponents are greater than 0, but less than one Negative Exponents can be written as fractions and decimals

Using Positive Exponents Expression Using Positive Exponents Value 102 100 101 10 1 10-1 1 . 0.1 10-2 0.01 10-3 103 0.001

Example = = =

Simplify