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# Exponents

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### Exponents

1. 1. EXPONENTS Zero and Negative
2. 2. X 2 X TO THE SECOND POWER OR X SQUARED X IS CALLED BASE 2 IS CALLED EXPONENT Use x as a factor 2 times X * X
3. 3. X 3 X TO THE THIRD POWER OR X CUBED X IS CALLED BASE 3 IS CALLED EXPONENT Use x as a factor 3 times X * X *X
4. 4. X 4 X TO THE FOURTH POWER X IS CALLED BASE 4 IS CALLED EXPONENT Use x as a factor 4 times X * X * X * X
5. 5. 3 2 3 TO THE SECOND POWER OR 3 SQUARED Use 3 as a factor 2 times 3 * 3 3 2 = 9
6. 6. 3 3 3 TO THE THIRD POWER OR 3 CUBED Use 3 as a factor 2 times 3 * 3 * 3 3 3 = 27
7. 7. POWERS OF BASE 10 10 0 = 1 10 1 = 10 10 2 = 100 10 3 = 1000 10 4 = 10,000 10 5 = 100,000 10 6 = 1,000,000
8. 8. POWERS OF BASE 2 2 0 = 1 2 1 = 2 2 2 = 4 2 3 = 8 2 4 = 16 2 5 = 32 2 6 = 64 Any base to the zero power equals 1 Any base to the one power equals itself 2 x 2 2 x 2 x 2 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 x 2
9. 9. POWERS OF BASE 3 3 0 = 1 3 1 = 3 3 2 = 9 3 3 = 27 3 4 = 81 3 5 = 243 3 6 = 729 Any base to the zero power equals 1 Any base to the one power equals itself 3 x 3 3 x 3 x 3 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 x 3
10. 10. TRY IT OUT 10 0 = 1 5 0 = 1 2 3 = 8 3 4 = 81 5 3 = 125 2 5 = 32
11. 11. TRY IT OUT 10 3 = 16 0 = 1 6 2 = 36 5 2 = 25 4 3 = 64 7 3 = 343 1000
12. 12. MULTIPLYING EXPONENTS WITH THE SAME BASE
13. 13. X 2 * X 3 = X 5 X * X * X * X* X Keep the base ADD the Exponents
14. 14. (10 2 ) (10 3 ) = 10 5 10 * 10 * 10 * 10* 10 Keep the base ADD the Exponents () () PARENTHESES mean TIMES
15. 15. (Y 3 X 2 ) (Y 4 X 3 ) = Y 7 X 5 ( Y * Y * Y * X * X ) * ( Y * Y* Y * Y * X * X * X) Keep the base ADD the Exponents () () PARENTHESES mean TIMES
16. 16. TRY IT OUT 5 * 5 2 * 5 3 = 5 6 Don’t forget the one exponent is implied X * Y 2 * X 3 * Y = X 4 Y 3 Don’t forget the one exponent is implied
17. 17. TRY IT OUT (XY 3 ) ( X 2 Y 3 ) = X 3 Y 6 Don’t forget the one exponent is implied (X 2 Y 2 Z 3 ) (Y 4 Z 5 ) = X 2 Y 6 Z 8 Don’t forget the one exponent is implied
18. 18. DIVIDING EXPONENTS WITH THE SAME BASE
19. 19. X 5 / X 3 = X 2 Keep the base SUBTRACT the Exponents
20. 20. 10 6 / 10 2 = 10 4 Keep the base SUBTRACT the Exponents
21. 21. Negative Exponents <ul><li>Negative exponents are NOT negative numbers </li></ul><ul><li>Negative exponents are fractions or decimals </li></ul><ul><li>Negative exponents are greater than 0 but less than one </li></ul>
22. 22. Examples 10 -3 = 1 10 3 OR 1 1000 OR 0.001
23. 23. Examples 2 -3 = 1 2 3 OR 1 8 OR 0.125
24. 24. Examples 2 -3 = 1 2 3 OR 1 8 OR 0.125 Negative Exponent To Reciprocal To Fraction To Decimal
25. 25. MORE EXAMPLES 10 –1 = 1 = 1 = 0.1 10 1 10 10 –2 = 1 = 1 = 0.01 10 2 100
26. 26. MORE EXAMPLES 10 –3 = 1 = 1 = 0.001 10 3 1000 10 –4 = 1 = 1 = 0.0001 10 4 10000
27. 27. MORE EXAMPLES 10 –5 = 1 = 1 = 0.00001 10 5 100,000 10 –6 = 1 = 1 = 0.000001 10 6 1,000,000
28. 28. Created by: pmastro.weebly.com/uploads/2/8/2/7/.../ exponents .801116. ppt