Exponents

6³ Exponent Base

(repeated multiplication) 6³ is read “Six Cubed” 6³ means 6 x 6 x 6 (repeated multiplication) 6³ = 216

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

Evaluate Exponents Evaluating Exponents: means to find the VALUE of. Example: 3² = -9º = (-3)³ = 9 -1 -27

Tricky Integer Bases = Exponents tell you how many times to multiply the base Positive Base Negative Base Evaluate: Evaluate: -9 9 ** Now check your answer with your calculators **

(-3) -3 (-3) • (-3) 9 (-3) • (-3) • (-3) -27 (-3) • (-3) • (-3) • (-3) Expression Expanded Form Evaluated Solution Expression Expanded Form Evaluated Solution (-3) -3   (-3) • (-3)  9  (-3) • (-3) • (-3)  -27  (-3) • (-3) • (-3) • (-3)  81 What patterns do you notice?

If you have a negative base and an odd exponent , the answer is negative. Example: If you have a negative base and an even exponent , the answer is positive. (-5)1 = -5 (-5)3 = -125 (-5)2 = 25 (-5)4 = 625

1 1 3 125 1 625 -9 100 16 1 -1 -7 -1

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. Why does x0 = 1?

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

Using Positive Exponents Expression Using Positive Exponents Value 102 100 101 10 1 10-1 1 . 10-2 10-3 103 1000

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

Negative Exponents Video Example = = = = Negative Exponents Video

Simplify