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Exponents

Exponents. Exponents. For Learning to Happen!. Remove all other thoughts from your mind. Pay close attention to this lesson. Try all of the examples. Ignore all other distractions. Exponents. An exponent is a little number high and to the right of a regular or base number. 3. 8.

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Exponents

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  1. Exponents

  2. Exponents For Learning to Happen! • Remove all other thoughts from your mind. • Pay close attention to this lesson. • Try all of the examples. • Ignore all other distractions.

  3. Exponents • An exponent is a little number high and to the right of a regular or base number. 3 8 Exponent Base

  4. Exponents This exponent is read 8 to the 3rd power, or 8 cubed. 3 8 Exponent Base

  5. Exponents An exponent tells how many times a number is multiplied by itself. 3 8 Exponent Base

  6. Exponents This exponent means 8•8•8 = 512 3 8 Exponent Base

  7. Exponents • This exponent is read • six to the fourth power. Exponent 6 4 Base

  8. Exponents • This exponent is read three to the 2nd power or three squared. Exponent 3 2 Base

  9. Exponents Read These Exponents 2 7 7 to the 2nd power or 7 squared

  10. Exponents Read These Exponents 3 10 10 to the 3rd power or 10 cubed

  11. Exponents What is the Exponent? 3 2 •2 • 2 = 2

  12. Exponents What is the Exponent? 4 a a •a • a • a=

  13. Exponents What is the Exponent? 3 (bc)(bc)(bc) = (bc) NOTICE that you keep the parenthesis around the variables (bc) because you are cubing all the (bc)

  14. Exponents Write the Verbal Phase Power Verbal Phrase Means “Seven to the 2nd power” “Seven squared” “Five to the 3rd power” “Five cubed”

  15. Exponents Write the Verbal Phase Power Verbal Phrase Meaning “Nine to the 4th power” “Two to the 5th power”

  16. Exponents How to Multiply Out Exponents = 3 •3 • 3 •3 4 3 9 27 81

  17. Exponents How to Multiply Out Exponents = 2 •2 • 2 •2 • 2 5 2 4 8 16 32

  18. Exponents When simplifying exponents you must watch the sign and the parenthesis! 62 = 6•6 –62 = –6•6 = 36 = -36 (-6)2 =(-6)(-6) -(6)2 = - (6)(6) = 36 1 = -36

  19. Exponents • An exponent is written in exponential form when it is simplified. Exponential Form 32a3

  20. Exponents • An exponent is written in factor form when it is written out. Factor Form 32a3 = 3•3•a•a•a

  21. Exponents Factored Form Exponential Form x • 8 • y • 8 • x 82x2y 2a2b1 a • b • a • 2 13 p p p r r 13p3r2

  22. Exponents Factored Form Exponential Form 5 • x • x • x 5x3 (5x)(5x)(5x) (5x)3 = 53x3 = 125x3

  23. Exponents Factored Form Exponential Form 8(ab)(ab) 8(ab)2 = 8a2b2 (4xwy)(4xwy)(4xwy) = 43x3w3y3 (4xwy)3 = 64x3w3y3

  24. Exponents Evaluate the expression if x = 3 and y = 4 “Evaluate” mean to solve!

  25. Exponents Evaluate the expression if x = 3 and y = 4 “Evaluate” mean to solve!

  26. Exponents Fractions With Exponents

  27. Exponents Fractions With Exponents

  28. Exponents Fractions With Exponents

  29. Exponents The End!!! Take out your Study Guide (blue).

  30. #1 Exponents 3 8 Exponent • An exponent tells how many times a number is • multiplied by itself. 8•8•8 = 512 Base Factored Form Exponential Form 3 • 3 • a • a • a • 32a3 x • y • x • 2 • 2x2y1

  31. # 2 Simplifying Powers When simplifying exponents you must watch the signand theparenthesis! 52 = 5•5 –52 =– (5)•(5) = 25 =–25 (-5)2 =(-5)(-5) = - (5)(5) –(5)2 =–25 = 25 1

  32. #3 1) 3) 2) 4) Evaluate The Power • To find 54 on my calculator I type in 5 ^ 4 = 625 5 4 = 625 xy 5 4 5 = 625 x 4 = 625 yx Circle the method that works on your calculator!

  33. TEACHER NOTE: The lesson above was taught for Pre-Algebra & Algebra.The following slides were used for the class of Algebra Readiness (lower level students) and slide #18-28 were taken out of the lesson above since we were just introducing Exponents.

  34. “Evaluate” mean to solve! 1) 3) 2) 4) Exponents Evaluate the Power

  35. Exponents Addition: -One-Dimensional Growth “Three added to four” = + 3 4 7 units = + Multiplication: Two-Dimensional Growth “Three times four” or “Three groups of four” + + = 3(4) 4 4 4 12 square units = = + +

  36. Exponents Exponents: Three-Dimensional Growth “Three to the third power” “Three to the fourth power” 3 3 3

  37. Perimeter Area Volume Exponents 5 5 5 5 5 5 5 5 5 P = s+s+s+s P = 4s “Five Squared” “Five Cubed” One Dimensional Two Dimensional Three Dimensional

  38. Exponents The End!!! I am going to give you a Study Guide (blue). Please take good notes on what we just learned! You can use these notes to help you with homework! You can use these notes on your test!

  39. #1 Exponents & Powers • An exponent or power tells how many • times a number is multiplied by itself. 4 Exponent 3 Base “Five to the 2nd power” “Five squared” “Seven to the 3rd power” “Seven cubed”

  40. #2 1) 3) 2) 4) Evaluate The Power • To find 54 on my calculator I type in 5 ^ 4 = 625 5 4 = 625 xy 5 4 5 = 625 x 4 = 625 yx Circle the method that works on your calculator!

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