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Simplifying and Evaluating Expressions with Power Property of Exponents

In this lesson, we explore the power property of exponents, which is crucial for simplifying and evaluating expressions. We review previous exponent rules such as ( x^0 = 1 ), ( x^1 = x ), ( x^m cdot x^n = x^{m+n} ), and the concepts of raising a power to a power. We introduce the power of a power property, power of a product, and power of a quotient properties, along with practical examples. Finally, we analyze expressions to confirm their equality. Master these concepts to enhance your algebraic skills!

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Simplifying and Evaluating Expressions with Power Property of Exponents

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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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