1. 7.3 MULTIPLICATION AND EXPONENTS: Base: A number that is multiplied repeatedly. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has.

2. GOAL:

3. Remember: An exponent equation has two components: Base Exponent

4. PROPERTIES: Multiplying powers with same base: For every number a≠0 and m, n, are integers, Ex: 1) 4 1 ∙ 4 3 2) 3 1 ∙ 3 -3 = 4 1+3 = 256 = 4 4 = 3 1+-3 = 3 -2

5. YOU TRY IT: Simplify: 1)12 4 ∙12 -2 2)(-2) 5 ∙ (-2) -2 3)m 3 ∙ m -1 ∙ m 5 4)9 -3 ∙ 9 2 ∙ 9 -4

6. SOLUTION: No matter what integer it is, anything to the power of zero is 1. 1)12 4 ∙12 -2  12 4-2  12 2  144 2) (-2) 5 ∙ (-2) -2 3) m 3 ∙ m -1 ∙ m 5  (-2) 5-2  (-2) 3  -8 4) 9 -3 ∙ 9 2 ∙ 9 -4  m 3-1+5  m 7  9 -3+2-4  9 -5

7. PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n )(b×10 m ) = a∙b×10 n+m

8. EXAMPLE: Simplify: 1)(5×10 4 )(12×10 -2 ) 2)(3×10 -5 )(4×10 -2 ) 3)(1.13×10 -7 )(9.8×10 5 )(3.34×10 22 )

9. SOLUTION: 1) (5×10 4 )(12×10 -2 ) 2) (3×10 -5 )(4×10 -2 ) 3) (1.13×10 -7 )(9.8×10 5 )(3.34×10 22 )  (5)(12)× 10 4-2  60× 10 2  6.0× 10 3  (3)(4)× 10 -5-2  12× 10 -7  1.2× 10 -6  (1.13)(9.8)(3.34)× 10 -7+5+22  36.99× 10 20  3.699× 10 21

10. VIDEO: Get a hot chocolate and enjoy this!!!. http://www.khanacademy.org/math/algebra/exponent- equations/exponent-properties-algebra/v/negative-and-positive- exponents

11. PROPERTIES: ZERO: as an exponent For every number a, Ex: 4 0 = 1 (-3) 0 = 1 100 0 = 1 1,000,000 0 = 1 -½ 0 =-1

12. PROPERTIES: Negative numbers: as an exponents For every nonzero number a≠0, and integer n Ex:

13. PROPERTIES: Multiplying powers with same base: For every number a≠0 and m, n, are integers, Ex: 1) 4 1 ∙ 4 3 = 4 1+3 = 4 4 = 256

14. PROPERTIES: Multiplying and Scientific notation For every nonzero number a, b and integer n and m (a×10 n )(b×10 m ) = a∙b×10 n+m

15. CLASSWORK: Page 424: Problems: 40, 41, 42 Page: 429: Problems: 9, 15, 24, 25, 29 33, 47.