1. Chapter 7 Review

2. x 0 = 1 Anything raised to the zero power = 1 1.)2.)

3. Negative Exponents * Switch Levels and then it is positive 1.) 2.) 5 -2 3.) If an exponent is negative it is sad where it is so we move it and then it is happy (positive)

4. Examples 1. x -5 2. 3x -3 q 3. x 3 y -4 4. 6x 3 y -1 q -7 4x

5. Evaluating with Exponents Plug in numbers Move negatives Simplify Ex.) x = 2, y = 4, z = -3

6. Try x = 5, y = -1, z = 6 1.)2.)

7. Standard to Scientific Notation 1. Find the factor between 1 and 10 2. Count the movements 3. Write as factor times ten raised to the number of movements

8. 1. ) 3,500 2.).00467

9. Try 1.) 6,700,000 2.).0023 3.).000045 4.) 175,000

10. Scientific to Standard Examples: 1. 3.4 x 10 9 2. 7.89 x 10 -5

11. Try 1. 3.4 x 10 8 2. 5.71 x 10 -5 3. 2.12 x 10 -3 4. 5.77 x 10 6

12. To multiply two powers that have the same base add the exponent 1.) 2 6 x 2 4 = 2 (6+4) = 2 10 2.) x 9 x x 7 =

13. Try 1.) (4 6 )(4 2 ) 2.) (x 9 )(x 3 ) 3.) (8 2 )(8 4 )

14. Product of Powers Multiply the constants Add the exponents of like variables 1.) 2.) (5x 3 y 2 )(6xy 3 ) =

15. Try 1.) (3x 6 )(2x) 2.) (4x 3 )(x 2 ) 3.) (9x 4 )(2x 4 )

16. Simplifying Monomials 1. Multiply and distribute all powers and parentheses 2. Combine like bases 3. Reduce all fractions

17. Example 1. (1/3xy)(-6y) 2. (2x) 5 (3x 2 )

18. 3. (1/2x 5 y 3 )(2/3xy 7 ) 4. (9x 5 y)(-2x 5 y 9 ) 2

19. Multiplying Numbers in Scientific Notation 1. Multiply Factors (number) 2. Add exponents 3. Make sure factor is still greater than 1 and less than ten (Put it in the calculator)

20. Example 1.) (3. 7 x 10 5 )(4.3 x 10 7 ) 2.) (4.9 x 10 4 )(5.6 x 10 -3 ) 3.) (1.2 x 10 6 )(1.1 x 10 6 )

21. Power of a Power Distribute to all terms! 1.) 2.) (x 3 ) 2 3.) (x 2 y 3 ) 9

22. Try 1. (x 3 ) 4 2. (x 2 ) 100 3. (x 3 y 4 ) 4 4. (x 5 ) 15

23. Power of a Product Distribute the exponent to each number and variable Simplify the number 1.)

24. Examples 2.) (4x 2 y 6 ) 3 3.) (2a 4 b 7 ) 4

25. Dividing Monomials When dividing monomials you subtract exponents with like bases. Example:

26. Examples 1. x 5 2. x 20 x 3 x 25 3. x 3 y 6 4. z 8 p 9 x 4 y 3 zp 6

27. When a fraction is in parentheses distribute the exponent to both the top and bottom Example:

28. Example 4 3 1. z 2 2. 5 pq x 4

29. Scientific Notation Put in your calculator! Examples: 1.) (3.45 x 10 4 ) x (4.56 x 10 8 ) 2.) (4.11 x 10 5 ) ÷ (3.23 x 10 7 )