1. Exponents: A quick short cut to multiplication! 7 4 Means 7 x 7 x 7 x 7 Means 7 is used as a factor 4 times!

2. 7 4 7 is the base 4 is the exponent The base is used as a factor 4 times.

3. Expanded notation: 5 x 5 x 5 x 5 x 5 x 5 Exponential notation: 5 6 Evaluated Notation: 15,625

5. -5 4 = ? (-5) 4 = ? Are they the same? Explain. -2 4 = ? (-2) 4 = ? Evaluate both.

6. (-5) 4 Will this value be negative or positive? (-5) 3 Will this value be negative or positive? Explain.

7. 3 2 x 3 5 Means 3 x 3 x 3 x 3 x 3 x 3 x 33 x 3 x 3 x 3 x 3 x 3 x 3 Can you see a short cut? Try it! 5 4 x 5 6 = ? 2 7 x 2 6 =?

8. 7 2 x 7 5 7 x 7 x 7 x 7 x 7 x 7 x 7 Or7 823,543

9. We can do this with variables also! w 3 w 2 Expand! w x w x w x w x w Exponential form: w5w5

10. (2a 2 ) (3a 5 ) Apply the commutative property to re- arrange the elements of the expression. 2 x 3 x a 2 x a 5 6a 7

11. Power of a Power (6 3 ) 4 Means this: 6 3∙ 6 3 ∙6 3 ∙6 3 Or 6 12

12. (4 5 ) 2 4 5 x 4 5 4 10 (52)4(52)4 52 x 52 x 52 x 5252 x 52 x 52 x 52 5858

13. 6 5 6 3 6 2 What about this? 7 5 7 5-5 = 7 0 = 1 7 5

14. Therefore anything to the zero power equals 1. 6 0 = 1 x 0 = 1 (ab) 0 = 1

15. Negative Exponents! 5 -3 = 1 5 3 ab -2 = a b 2 12 7 = 12 7-10 = 12 -3 = 1 12 10 12 3