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Bell Ringer

Bell Ringer. Solve. 1. 5x + 18 = -3x – 14 +3x +3x 8x + 18 = -14 - 18 -18 8x = -32 8 8 x = -4. 2. 7(x + 3)= 105 7x + 21 = 105 -21 -21 7x = 84

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Bell Ringer

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  1. Bell Ringer • Solve. 1. 5x + 18 = -3x – 14 +3x +3x 8x + 18 = -14 - 18 -18 8x = -32 8 8 x = -4 2. 7(x + 3)= 105 7x + 21 = 105 -21 -21 7x = 84 7 7 x = 12

  2. Quiz Results • Since there are still a few who haven’t taken the quiz, I’ll give out the results as soon as they do. • If you want to know your grade, log onto your Gradebook and check it yourself. • Otherwise, you’ll have to wait… • NO, I’m not digging through the papers to tell you your grade.

  3. NCP 503: Work with numerical factors NCP 505: Work with squares and square roots of numbers NCP 506: Work problems involving positive integer exponents* NCP 504: Work with scientific notation NCP 507: Work with cubes and cube roots of numbers NCP 604: Apply rules of exponents Exponents and Radicals

  4. Basic Terminology Exponent 34 = 3•3•3•3 = 81 Its read, “Three to the fourth power.” Base The base is multiplied by itself the same number of times as the exponent calls for.

  5. Important Examples -34 = –(3•3•3•3) = -81 (-3)4 = (-3)•(-3)•(-3)•(-3) = 81 -33 = –(3•3•3) = -27 (-3)3 = (-3)•(-3)•(-3) = -27

  6. Variable Expressions x4 = x • x • x • x y3 = y • y • y Evaluate each expression if x = 2 and y = 5 x4y2 = 400 = (2•2•2•2)•(5•5) 3xy3 = 750 = 3•2•(5•5•5)

  7. Laws of Exponents, Pt. I Zero Exponent PropertyNegative Exponent PropertyProduct of PowersQuotient of Powers

  8. Zero Exponent Property Any number or variable raised to the zero power is 1. x0 = 1 y0 = 1 z0 = 1 70 = 1 -540 = 1 1230 = 1

  9. Negative Exponent Any number raised to a negative exponent is the reciprocal of the number. x-1 = y-1 = 5-1 = x-2 = 3-2 = = 5-3 = = 1 5 1 X 1 y 1 X2 1 53 1 32 1 9 1 . 125

  10. Negative Exponent 3x-3 = 5y-2 = 2x-2y2= 3-2 x4= 5 y2 3 x3 Only x is raised to the -3 power! 2y2 x2 x4 32 x4 9 = Only x is on the bottom.

  11. Product of Powers This property is used to combine 2 or more exponential expressions with the SAME base. Multiplication NOT Addition! 53•52 = (5•5•5)•(5•5) = 55 x4•x3 = (x•x•x•x)•(x•x•x) = x7 If the bases are the same, add the exponent!

  12. Product of Powers Product of powers also work with negative exponents! 1 62•63 1 7776 1 65 = = 6-2•6-3 = 1 x5•x7 1 x12 = x-5•x-7 = n-3•n5 = n-3+5 = n2

  13. Quotient of Powers This property is used when dividing two or more exponential expressions with the same base. x6 x3 = x6-3 = x3 Subtract the exponents! (Top minus the bottom!)

  14. Quotient of Powers 67 65 = 36 = 67-5 = 62 x3 x5 1 x2 = x3-5 = x-2 = OR x3 x5 x ∙ x ∙ x x∙x∙x∙x∙x 1 x2 = =

  15. Power of a Power Power of a Product Power of a Quotient Laws of Exponents, Pt. II

  16. Power of a Power This property is used to write an exponential expression as a single power of the base. (63)4 = 63•63•63•63 = 612 (x5)3 = x5•x5•x5 = x15 When you have an exponent raised to an exponent, multiply the exponents!

  17. Power of a Power Multiply the exponents! = 532 (54)8 = n12 (n3)4 = 36 (3-2)-3 1 x15 = = x-15 (x5)-3

  18. Power of a Product Power of a Product – Distribute the exponent on the outside of the parentheses to all of the terms inside of the parentheses. (xy)3 (2x)5 = x3y3 = 25 ∙ x5 =32x5 (xyz)4 = x4 y4 z4

  19. Power of a Product More examples… (x3y2)3 (3x2)4 = x9y6 = 34 ∙ x8 =81x8 • (3xy)2 • = 32∙ x2 ∙ y2 =9x2y2

  20. Power of a Quotient Power of a Quotient – Distribute the exponent on the outside of the parentheses to the numerator and the denominator of the fraction. ) ( ) ( x y x5 y5 5 =

  21. Power of a Quotient More examples… ) ( ) ( 2 x 8 x3 23 x3 3 = = ) ( ( ) 3 x2y 34 x8y4 4 81 x8y4 = =

  22. Basic Examples

  23. Basic Examples

  24. Basic Examples

  25. More Difficult Examples

  26. More Examples

  27. More Examples

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