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# Laws of Exponents

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### Laws of Exponents

1. 1. Today’s Objective: <ul><li>SWBAT multiply and divide powers. </li></ul>
2. 2. Multiplication: <ul><li>10 2 ∙10 3 =? </li></ul><ul><li>3 6 ∙3 5 =? </li></ul><ul><li>2 10 ∙2 7 =? </li></ul>
3. 3. Multiplication: <ul><li>10 2 ∙10 3 = 100,000= 10 5 </li></ul><ul><li>3 6 ∙3 5 = 177,147= 3 11 </li></ul><ul><li>2 10 ∙2 7 = 131,072= 2 17 </li></ul><ul><li>Do you see any pattern? </li></ul>
4. 4. Product of Powers Rule: <ul><li>b m ∙b n = b m+n </li></ul><ul><li>When multipying exponents, you can add the exponents ONLY if the bases are the SAME! </li></ul>
5. 5. Division: <ul><li>10 6 ÷ 10 3 =? </li></ul><ul><li>3 7 ÷ 3 5 =? </li></ul><ul><li>2 10 ÷ 2 7 =? </li></ul>
6. 6. Division: <ul><li>10 6 ÷10 3 = 1,000= 10 3 </li></ul><ul><li>3 7 ÷3 5 = 9= 3 2 </li></ul><ul><li>2 10 ÷2 7 = 8= 2 3 </li></ul><ul><li>Do you see any pattern? </li></ul>
7. 7. Quotient of Powers Rule: <ul><li>b m b n When multipying exponents, you can add the exponents ONLY if the bases are the SAME! </li></ul>= b m-n
8. 8. ZERO Exponent: <ul><li>For every nonzero #: a 0 =1 </li></ul>
9. 9. NEGATIVE Exponent: <ul><li>For every nonzero #: a -n = 1_ a n </li></ul>
10. 10. Simplify: <ul><li>b 0 d 3 b 2 d </li></ul>
11. 11. Simplify: <ul><li>b 0 d 3 b 2 d </li></ul><ul><li>b 0 b 2 d 3 d </li></ul>
12. 12. Simplify: <ul><li>b 0 b 2 d 3 d </li></ul>
13. 13. Simplify: <ul><li>b 0 b 2 d 3 d </li></ul><ul><li>b 2 d 4 </li></ul>
14. 14. Simplify: <ul><li>b 4 d 3 b -2 d -3 </li></ul>
15. 15. Simplify: <ul><li>b 4 d 3 b -2 d -3 </li></ul><ul><li>b 4 b -2 d -3 d 3 </li></ul>
16. 16. Simplify: <ul><li>b 4 b -2 d -3 d 3 </li></ul>
17. 17. Simplify: <ul><li>b 4 b -2 d -3 d 3 </li></ul><ul><li>b 2 d 0 </li></ul>
18. 18. Simplify: <ul><li>b 2 d 0 </li></ul><ul><li>b 2 </li></ul>