7-Chapter Notes

1. 7-Chapter Notes Algebra 1

2. 7-1 Notes for Algebra 1 Multiplication properties of Exponents

3. 7.1 pg. 395 21-63o, 69-84(x3)

4. Monomial (only one term) A number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. An expression that involves division by a variable is not a monomial.

5. Constant A monomial that is a real number.

6. Example 1: Identify Monomials Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1.) 2.) 3.) 4.)

7. Example 1: Identify Monomials Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1.) No, it involves subtraction, so it has more than one term. 2.) Yes, it involves the product of a number and two variables. 3.) Yes, the expression is a constant. 4.) No, it has a variable in the denominator.

8. Product of Powers To multiply two powers that have the same base, add their exponents.

9. Example 2: Product of Powers Simplify each expression. 1.) 2.)

10. Example 2: Product of Powers Simplify each expression. 1.) 2.)

11. Power of a Power To find the power of a power, multiply the exponents.

12. Example 3: Power of a Power Simplify

13. Example 3: Power of a Power Simplify

14. Power of a Product To find the power of a product, find the power of each factor and multiply.

15. Example 4: Power of a Product Express the volume of a cube with side length as a monomial.

16. Example 4: Power of a Product Express the volume of a cube with side length as a monomial.

17. Simplify Expressions To simplify a monomial expression, write an equivalent expression in which: • Each variables base appears exactly once, • There are no powers of powers, and • All fractions are in simplest form.

18. Example 5: Simplify Expressions Simplify:

19. Example 5: Simplify Expressions Simplify:

20. 7.2 Notes for Algebra 1 Division Property of Exponents

21. 7.2 pg. 403 19-57o, 66-87(x3)

22. Quotient of Powers To divide two powers with the same base, subtract the exponents.

23. Example 1: Quotient of Powers Simplify.

24. Example 1: Quotient of Powers Simplify.

25. Power of a Quotient To find the power of a quotient, find the power of a numerator and the power of the denominator.

26. Example 2: Power of a Quotient Simplify.

27. Example 2: Power of a Quotient Simplify.

28. Zero exponent Any nonzero number raised to the zero power is equal to 1.

29. Example 3: Zero Exponent Simplify. 1.) 2.)

30. Example 3: Zero Exponent Simplify. 1.) 1 2.)

31. Negative Exponent Property For any nonzero number and any integer

32. Example 4: Negative Exponents Simplify. 1.) 2.)

33. Example 4: Negative Exponents Simplify. 1.) 2.)

34. Order of Magnitude (used to compare measures to estimate and preform rough calculations) The quantity of a number rounded to the nearest power of 10

35. Example 5: Apply Properties of Exponents Darin has $123,456 in his savings account. Tab has $156 in his savings account. Determine the order of magnitude of Darin’s account and Tab’s account. How many orders of magnitude as great is Darin’s account as Tab’s account?

36. Example 5: Apply Properties of Exponents Darin has $123,456 in his savings account. Tab has $156 in his savings account. Determine the order of magnitude of Darin’s account and Tab’s account. How many orders of magnitude as great is Darin’s account as Tab’s account? Darin’s: Tab’s: Darin’s account is 3 orders of magnitude as great as Tab’s account.

37. 7-3 Notes for Algebra 1 Rational Exponents

38. 7-3 pg. 410 17-83o, 96-114(x3)

39. Rational exponents For any nonnegative real number ,

40. Example 1: Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. 1.) 2.) 3.) 4.)

41. Example 1: Radical and Exponential Forms Write each expression in radical form, or write each radical in exponential form. 1.) 2.) 3.) 4.)

42. th root For any real numbers and and any positive integer . If , then is the th root of .

43. Example 2: th roots Simplify. 1.) 2.)

44. Example 2: th roots Simplify. 1.) 2.)

45. For any positive real number and any integer

46. Example 3: Evaluate Expressions Simplify. 1.) 2.)

47. Example 3: Evaluate Expressions Simplify. 1.) 2.)

48. For any positive real number and any integer and or

49. Example 4: Evaluate Expressions Simplify. 1.) 2.)

50. Example 4: Evaluate Expressions Simplify. 1.) 2.)