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Bell Ringer

Bell Ringer. Solve. 1. 6 x – 8 = -4x + 22 + 4 x +4x 2x – 8 = 22 + 8 + 8 2x = 30 2 2 x = 15. 2. -3(x – 6)= 3 -3x + 18 = 3 – 18 – 18 -3x = -15 -3 -3 x = 5. Homework. n 4 4x 6 y 5 7y 2 /x 3 3

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Bell Ringer

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  1. Bell Ringer • Solve. 1. 6x – 8 = -4x + 22 +4x +4x 2x – 8 = 22 + 8 + 8 2x = 30 2 2 x = 15 2. -3(x – 6)= 3 -3x + 18 = 3 – 18 – 18 -3x = -15 -3 -3 x = 5

  2. Homework • n4 • 4x6y5 • 7y2/x3 • 3 • 1728 • 2x • 2x2 • -4/y2 • 5y/x2 • 2y2/x5 • 3x7/y2 • 6x2/y3z3 • 16 • 80 • 512 • 3/16 • x3 • y4 • 15x12 • 1/c9 • 1296 • -1296 • 1/27 • 4096 • 1 • 1/125 • 1 • -128

  3. Laws of Exponents, Pt. I Review! Zero Exponent PropertyNegative Exponent PropertyProduct of PowersQuotient of Powers

  4. Laws of Exponents, Pt. 1 Zero Exponent Property – Any number raised to the zero power is 1. x0 = 1 30 = 1 120 = 1 Negative Exponent Property – Any number raised to a negative exponent is the reciprocal of the number. x-1 = 5-3 = 3x2y-3 = 3x2 y3 1 x 1 53

  5. Laws of Exponents, Pt. 1 Product of Powers – When multiplying numbers with the same bases, ADD the exponents. Quotient of Powers – When dividing numbers with the same bases, SUBTRACT the exponents. x2•x8 = x10 3x4•x-2 = 3x2 x6 x2 10x4y3 2x7y 5y2 x3 = x4 =

  6. Bonus! Solve the problem in pieces. 30 x6 y2 z5 6 x3 y5 z8 5x3 y3z3 = 1. Whole numbers 2. x 3. y 4. z 10 x2 z6 15 x5 y3 2z6 3x3y3 =

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

  8. 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!

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

  10. 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

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

  12. 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 =

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

  14. Basic Examples

  15. Basic Examples

  16. Basic Examples

  17. More Difficult Examples

  18. More Examples

  19. More Examples

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