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exponential Fun: An Interactive Tutorial on the Properties of Exponents

exponential Fun: An Interactive Tutorial on the Properties of Exponents. Click here to begin. objective. to learn how to multiply and divide expressions with exponents, including zero and negative exponents. Tennessee State Standards: 1.0 Number and Operations

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exponential Fun: An Interactive Tutorial on the Properties of Exponents

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  1. exponential Fun: An Interactive Tutorial on the Properties of Exponents Click here to begin

  2. objective to learn how to multiply and divide expressions with exponents, including zero and negative exponents. Tennessee State Standards: 1.0 Number and Operations 1.1 demonstrate an understanding of the subsets, properties, and operations of the real number system 1.1d use exponents to simplify a monomial written in expanded form 1.2 demonstrate an understanding of the relative size of rational and irrational numbers 1.2f select ratios and proportions to represent real-world problems (e.g. scale drawings, sampling, etc.) 2.0 Algebra 2.2 use algebraic thinking to generalize a pattern by expressing the pattern in functional notation 2.2i Evaluate an algebraic expression given values for one or more variables using grouping symbols and/or exponents less than four

  3. Read the tutorial and complete the quiz at the end to test your knowledge! takes you to the directions page takes you to the main menu takes you to the next page takes you back to the previous slide stops the lesson directions

  4. main menu

  5. an expression like 46 is called a power. The exponent 6 represents the number of times the base 4 is used as a factor: exponent base 46 = 4 ● 4 ● 4 ● 4 ● 4 ● 4 power6 factors of 4 expressions containing exponents

  6. Let a and b be numbers and let m and n be integers: to multiply two powers that have the same base add the exponents together: a2a3 = a2 ● a3 = a ● a ● a ● a ● a 2 factors 3 factors = a3+ 2 = a5 multiplying exponents:product of powers property

  7. Let a and b be numbers and let m and n be integers: to find the power of a power, you multiply exponents: (a2)3 = a2● a2● a2 3 factors = a ● a ● a ● a ● a ● a 6 factors = a6 =(a2)3 multiplying exponents:power of a power property

  8. to find the power of a power, you multiply exponents Important Note: when you use the power of product property, it is the quantity within the parentheses that is raised to the power, not the individual terms. For example: (a + 1)3 has 3 factors: (a + 1)3 = (a + 1)(a + 1)(a + 1) multiplying exponents:power of a power property

  9. Let a and b be numbers and let m and n be integers: to find the power of a product, find the power of each factor and multiply: (a ● b)3 = a3● b3 (ab)3 = a3b3 multiplying exponents:power of a product property

  10. Let a and b be numbers and let m and n be integers: Let a be a nonzero number and let n be a positive integer: A nonzero number to the zero power is 1: a0 = 1, a = 0. a-n is the reciprocal of an: a-n = 1/an, a = 0. zero and negative exponents

  11. Let a and b be numbers and let m and n be integers: to divide powers having the same base, subtract exponents: am/an = am – n, a = 0 dividing with exponents:quotient of powers property

  12. Let a and b be numbers and let m and n be integers: to find a power of a quotient, find the power of the numerator and the power of the denominator and divide: (a/b)m = am/bm, b = 0 dividing with exponents:power of a quotient property

  13. Now that you have learned how to multiply and divide expressions with exponents, including zero and negative exponents, check your understanding with these quiz questions! Time for a quiz!

  14. Simplify the following expression: (4x2y)3● x5 quiz question one a. 4x10y3 b. 4x7y3 c. 64x11y3 d. 64x10y3

  15. The correct answer is c: (4x2y)3● x5 = 43● (x2)3● y3● x5 power of a product = 64 ● x6● y3●x5power of a power = 64x11y3product of powers Great job!

  16. Remember the rules: To multiply two powers that have the same base, add the exponents together. To find the power of a power, you multiply exponents. To find the product of a power, find the power of each factor and multiply. Try again…

  17. Simplify the following expression: (abc2)3(a2b)2 quiz question two a. a5b5c5 b. a7b5c6 c. a12b6c6 d. a7b5c5

  18. The correct answer is b: (abc2)3(a2b)2 = a3b3(c2)3● a4b2 power of a product =a3b3c6● a4b2 power of a power =a7b5c6 product of powers Great job!

  19. Remember the rules: To multiply two powers that have the same base, add the exponents together. To find the power of a power, you multiply exponents. To find the product of a power, find the power of each factor and multiply. Try again…

  20. You are offered a job that pays 2x dollars or 2x dollars for x hours of work. Assuming you must work at least 2 hours, which method of payment would you choose? quiz question three a. 2x dollars b. 2x dollars

  21. The correct answer is b. If you work more than 2 hours, the pay is much better at the rate of 2x dollars per hour. For example, at 2x dollars per hour, you would earn $256 for 8 hours: 28 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 ● 2 ● 2 = 256 while at 2x dollars per hour , you would earn $16: 2 ● 8 = 16 Great job!

  22. Remember the rules: an expression like 46 is called a power. The exponent 6 represents the number of times the base 4 is used as a factor: exponent base 46 = 4 ● 4 ● 4 ● 4 ● 4 ● 4 power 6 factors of 4 Try again…

  23. Evaluate the exponential expression: 3-2● 32 quiz question four a. 0 b. 6 c. 3 d. 1

  24. The correct answer is d: 3-2● 32 =3-2 + 2 product of powers = 30 add exponents = 1 a0 is 1 Great job!

  25. Remember the rules: To multiply two powers that have the same base, add the exponents together. A nonzero number to the zero power is 1: a0 = 1, a = 0. Try again…

  26. Evaluate the exponential expression: (5a)-2 quiz question five a. 5a/2 b. 1/25a2 c. 25a/2 d. a2/5

  27. The correct answer is b: (5a)-2 = 5-2● a-2power of a product = 1/52● 1/a2 reciprocals of 52and a2 = 1/25a2 multiply fractions Great job!

  28. Remember the rules: To find the product of a power, find the power of each factor and multiply. a-n is the reciprocal of an: a-n = 1/an, a = 0 Try again…

  29. Evaluate the exponential expression: 94 ●92/97 quiz question six a. 9 b. 1 c. 1/9 d. 96/7

  30. The correct answer is c: 94 ● 92/97 = 94+2/97 = 96/97 product of powers = 9-1quotient of powers = 1/9 Great job!

  31. Remember the rules: To multiply two powers that have the same base, add the exponents together. To divide powers having the same base, subtract exponents. Try again…

  32. Evaluate the exponential expression: (7/4)-3 quiz question seven a. -7/4 b. 4/7 c. 64/343 d. 343/64

  33. The correct answer is c: (7/4)-3 = 7-3/4-3 power of a quotient = 43/73definition of negative exponents = 64/343 Great job!

  34. Remember the rules: To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. Try again…

  35. Evaluate the exponential expression: 2x2y/3x ● 9xy2/y4 quiz question eight: put it all together! a. 6x2/y b. 18x2/y c. x2/6y d. 6x/y2

  36. The correct answer is a: 2x2y/3x ● 9xy2/y4 = (2x2y)(9xy2)/(3x)(y4) = 18x3y3/3xy4product of powers = 6x2y-1quotient of powers =6x2/ydefinition of negative exponents Great job!

  37. Remember the rules: to multiply two powers that have the same base add the exponents together to divide powers having the same base, subtract exponents a-n is the reciprocal of an: a-n = 1/an, a = 0 Try again…

  38. Summary Now you know how to multiply and divide expressions with exponents, including zero and negative exponents.

  39. resources Algebra I Teacher's Edition. Larson, R., Boswell, L., Kanold, T.D. and Stiff, L. 2004, Evanston, McDougal Littell. all images under license from Fotolia.com

  40. good job! You have completed the tutorial. Please click on the exit button to exit out of the program. exit

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