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Lesson 40

Lesson 40. Simplifying and evaluating expressions using the power property of exponents. Previous lessons involving exponents. x 0 = 1 x 1 = x x m x n = x m+n x m = x m-n x n x -n = 1 x n. Raising a power to a power. (2 4 ) 3 means 2 4 2 4 2 4 = 2 12

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Lesson 40

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  1. Lesson 40 Simplifying and evaluating expressions using the power property of exponents

  2. Previous lessons involving exponents • x0 = 1 • x1 = x • xm xn = x m+n • xm= xm-n • xn • x-n= 1 • xn

  3. Raising a power to a power • (24)3 means 24 24 24 = 212 • (32)3 means 32 32 32 = 36 • (a3)5 means a3 a3 a3 a3 a3 = a15

  4. Write a rule for raising a power to a power • (x3)2 (d4)4 • (s3)2 (b6)3 • (102)3 (c5)6

  5. Power of a power property (power rule) • If m and n are real numbers and x does not equal 0, then • (xm)n = xmn

  6. Power of a product property • If m is a real number with x not equal to 0 and y not equal to 0, then • (xy)m = xmym

  7. simplify • (7a3b5)3 • (-2y4)3 • (3g4)3 • (-4m2n3)2

  8. Power of a quotient property • If x and y are nonzero real numbers and m is an integer, then • x m = xm • y ym

  9. simplify • 2x 2-x24 • 5 3y

  10. simplify • (4xy2)2(2x3y)2 • (-5x-2)2(3xy2)4 • (2xy3)2(5x2y)3 • (-4x-3)2(6xy2)3

  11. question • Is 5(x2)3 = (5x2)3 ?

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