1. Laws of Exponents

2. Vocabulary Factor:an integer that divides into another integer with no remainder. Factor:an integer that divides into another integer with no remainder. 24 1, 2, 3, 4, 6, 8, 12, 24

3. Exponent:tells how many times to multiply a number by itself Exponent:tells how many times to multiply a number by itself Base:the number that is multiplied by itself Base:the number that is multiplied by itself Power:an expression using a base and an exponent Power:an expression using a base and an exponent 4545 = 4 4 4 4 4 2 6 6363

4. Expressions with Exponents (-6) 4 (-6) 4 -6 4 -6 4 (-6) (-6) (-6) (-6) -(6) (6) (6) (6) *They are not the same. 36 36 -(36 36) 1,296 1,296 -1,296 -1,296

5. Exponents and Multiplication To Multiply powers with the SAME base: To Multiply powers with the SAME base: **Add the exponents and keep the base** Examples: 1) 3 2 ∙ 3 6 = 3 8 2) a m ∙ a n = a m + n 2) a m ∙ a n = a m + n

6. Exponents and Division To Divide powers with the SAME base: **Subtract the exponents and keep the base** **Subtract the exponents and keep the base** Examples: 1) 8 5 = 8 2 8 3 8 3 2) a m = a m - n a n a n

7. Zero as an Exponent For any non-zero number a, a 0 = 1 For any non-zero number a, a 0 = 1 Examples: 1) 9 0 = 1 Examples: 1) 9 0 = 1 2) 15 0 = 1 2) 15 0 = 1 3) 1 0 = 1 3) 1 0 = 1

8. Negative Exponents For any non-zero number a and integer n, For any non-zero number a and integer n, a –n = 1 a n a n Example: 8 -5 = 1 8 5 8 5