1. COMPETENCY #2 Laws of Exponents Scientific Notation

2. 5 2 = 5 x 5 =25 3 4 =3 x 3 x 3 x 3 = 81 7 3 = 7 x 7 x 7 = 343

3. 5 2 x 5 4 (5 x 5)(5 x 5 x 5 x 5) = 5 6 Do you see a pattern or shortcut?

4. 3 3 x 3 5 (3x3x3)(3x3x3x3x3) = 3 8 Do you see a pattern or shortcut?

5. a 3 x a 5 (a x a x a)(a x a x a x a x a) = a 8 Do you see a pattern or shortcut?

6. Product of Powers Property To multiply powers (exponents) with the same base, add their exponents. a³ x a²= a 3 + 2 = a 5

7. 2525 2323 = 2 x 2 x 2 x 2 x 2 2 x 2 x 2 = 2 1 4545 4242 = 4 x 4 x 4 x 4 x 4 4 x 4 = 4343 1 Do you see a pattern or shortcut?

8. Quotient of Powers Property To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. 6 8 = 6 8-5 =6 3 6 5

9. REVIEW When multiplying- add the exponents When dividing- subtract the exponents.

10. EXAMPLES 2 3 2 2 = 69=69= 6464 z5z5 b 10 2525 6565 b 7 b 3 = Z 8 = z 3

11. Zero Exponents For any nonzero number a, a 0 = 1 Anything to the zero power equals 1 (except zero) 4 0 = 100 0 = 1 1

12. Negative Exponents For any nonzero number a and any integer n, a -n = 1/a n 5 -2 = 1 5252

13. 3 -5 = 1 3535 5 -2 = 1 5252 3y -2 =3 y2y2 a -7 b 3 =b3b3 a7a7

14. 5 -8 x 5 -3 = 5 -8 + -3 =5 -11 5 11 1 or a -2 x a 10 = a -2 + 10 =a8a8

15. b -8 x b 5 = b -8 + 5 =b -3 b3b3 1 or 3 -4 x 3 11 = 3 -4 + 11 =3737

16. 3535 3838 = 3 5 - 8 = 3 -3 or 1 3 a6a6 a -2 = a 6 – (-2) = a8a8 m2m2 m -4 = m 2 – (-4) = m6m6

17. Scientific Notation is a short hand way of writing numbers using powers of 10

18. Standard ProductScientific NotationFormNotation 120,000,000 1.2 x 10 8 1.2 x 100,000,000

19. Write in scientific notation. 46,200,000,000 = 4.62 x 10 9 Where is the decimal now? Move the decimal to the right of the first significant digit.

20. Write in scientific notation. 89,000,000 = 8.9 x 10 7 Where is the decimal now? Move the decimal to the right of the first significant digit.

21. Write in scientific notation. 304,000,000,000 = 3.04 x 10 11 Where is the decimal now? Move the decimal to the right of the first significant digit.

22. Standard ProductScientific NotationFormNotation 0.00056 5.6 x 10 -4 5.6 x 0.0001

23. Write in scientific notation. 0.00000052 = 5.2 x 10 -7 Move the decimal to the right of the first significant digit. # is less than 1 so exponent is negative

24. Write in scientific notation. 0.00000000106 = 1.06 x 10 -9 Move the decimal to the right of the first significant digit. # is less than 1 so exponent is negative

25. 3.2 x 10 7 = Positive Exponents move the decimal to the right 3 2000000 Write in standard form. Count the # of spaces to move and fill in with zeros.

26. 6.04 x 10 5 = Positive Exponents move the decimal to the right 6 0 4000 Write in standard form. Count the # of spaces to move and fill in with zeros.

27. 1.3 x 10 -5 = Negative Exponents move the decimal to the left. # less than 1. 1 30000 Write in standard form. Count the # of spaces to move left and fill in with zeros. Then add a decimal point

28. 2.07 x 10 -4 = Negative Exponents move the decimal to the left. # less than 1. 2 0 7000 Write in standard form. Count the # of spaces to move left and fill in with zeros. Then add a decimal point

29. Write these in scientific notation. 4100 4.1 x 10 3 0.0000676.7 x 10 -5 62,000,0006.2 x 10 7 0.000000003 3 x 10 -9

30. Write these in standard form. 3.04 x 10 3 3,040 7.2 x 10 5 720,000 5 x 10 -3 0.005 3.8 x 10 -6 0.0000038