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Properties of ExponentsExamples and Practice
Product of Powers PropertyHow many factors of x are in the product x3∙x2? Write the product as a single power. In general: 5 factors: x∙x∙x∙x∙x x∙x∙x∙x∙x = x5 xm∙xn= xm + n
Question #1 Simplify the expression: a3a5 a. a15 b. a8 c. a2 d. 1/a2
Question #2 Simplify the expression: (3m2)(2m4) a. 6m8 b. 5m6c. 5m8 d. 6m6
Question #3 Simplify the expression: (-2xy3)(5x4y2)a. -10x5y5 b. -10x4y5 c. 3x5y5 d. -10x4y6
Power of a Power PropertyHow many factors of x are in the expression (x3)2? Write the product as a single power. In general: 6 factors: x∙x∙x∙x∙x∙x (x∙x∙x)∙(x∙x∙x) = x6 (xm)n= xm∙n
Question #4 Simplify the expression: (42)5 a b c d. 167
Question #5 Simplify the expression: (x3)4 a. x7 b. 2x7 c. x12 d. 2x12
Power of a Product PropertyHow many factors of x and y are in the expression (xy)2? Simplify the expression. In general: 2 factors of each: (x∙y)∙(x∙y) (x∙y)∙(x∙y) = x2y2 (x∙y)m= xmym
Question #6 Simplify the expression: (b3c2)4 a. b7c6 b. b12c8c. b7c8 d. 2b12c8
Question #7 Simplify the expression: (-3a3b)2 a. 6a5b2 b. 9a5b2c. -9a6b2 d. 9a6b2
Question #8 Simplify the expression: (-3a3b)2(2ab) a. 36a7b3 b. 18a7b3c. -6a7b3 d. -18a7b3
Quotient of Powers PropertySimplify the expression. In general:
Question #9 Simplify the expression: a. a5 b. a9 c. 1/a5 d. 1/a9
Question #10 Simplify the expression: a. a5 b. 6 c. 1/a5 d. 1/6
Question #11 Simplify the expression: a. -3a5 b. -16a5c. -3a8 d. -16a8
Question #12 Simplify the expression: a. b. c. d a4b3
Power of a Quotient PropertySimplify the expression. In general:
Question #13 Simplify the expression: a. b. c. d
Question #14 Simplify the expression: a. b. c. d.
Negative Exponent PropertyIn general:
Question #15 Simplify the expression: (34)(3-2) a. 38 b. 3-8c d. 32
Question #16 Simplify the expression: a. b. c. d.
Question #17 Simplify the expression: a b. 26 c d.
Question #18 Simplify the expression: a. b. c. d.
Question #19 Simplify the expression: a. b. c. d.
Zero Exponent PropertyIn general:
Question #20 Simplify the expression: x0y-2 a. b. xy2 c. y2 d.
Properties of Exponents
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7.2 Properties of Rational Exponents OBJ: use properties of rational exponents & radicals and write expressions in simplest form Do Now: Simplify a)(-5)
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Evaluate the expression. Tell which properties of exponents you used.
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Be able to multiply monomials. Be able to simplify expressions involving powers of monomials.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Exponents and Polynomials
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8.7/8.8 DIVISION AND MORE MULTIPLICATION PROPERTIES OF EXPONENTS ALGEBRA 1 CP OBJECTIVE: USE TWO MORE MULTIPLICATION PROPERTIES AND APPLY DIVISION PROPERTY.
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Bell Problem Simplify 13, Use Properties of Exponents Standards: 1.Understand ways of representing numbers 2. Understand how operations are.
Multiplying and Dividing Monomials 4.3 Monomial: An expression that is either a: (1) numeral or constant, ex : 5 (2)a v ariable, ex: x (3)or a product.
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