Chapter 7: Exponents

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1 Chapter 7: Exponents Algebra 1 Chapter 7 Notes Name: Algebra Homework: Chapter 7 (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework Section 7.: Scientific Notation M 1 Section 7.: Multiplication Properties of /1 Exponents T /1 Review of Sections Section 7.: Raising a Power to a Power Combine Like Terms HW #1: Pg. 6: -6, 7-1 odd, 1, 16, 1- Pg. 1: 1-, 8-6 even, - all, 8, 9 HW #: Pg. 7: -0 even Pg. 68: 1-0 even Pg. 78: - even W /16 Review of Sections Section 7.: Division Properties of Exponents Multiply and combine like terms HW# Pg. : 1- all, 6-8 even (SKIP 0) Pg. 6: - even Pg. 68: 1-19 odd Chapter 7 Test on Tuesday 11/. Th /17 Chapter 7 Review HW# Ch. 7 Study Guide Correct Study Guide Online in PEN Chapter 7 Test on Tuesday 11/ Print Chapter 8 Notes by Wednesday F /18 Chapter 7 Test HW# Pg. 6: 1-7 odd Pg. 68: -0 even Print: Chapter 8 Notes by Tomorrow 1

2 Notes #1: Sections Section 7.1: Review Algebra 1 Chapter 7 Notes Simplify; leave all answers in positive exponents: 1.) m -.) y -1.) 6m 0.) -.) - 6.) ) (7m ) 0 8.) 0 x y Evaluate if a = - and b = -: 9.) a b ) ab ) a -1 + b -1 1.) (ab) - Section 7.: Review Write in Scientific Notation: 1.) 76,000.) 1 7. x 10.) 0.00 x Write in Scientific Notation: 6.) ),000 6.) 0.6. x 10 7.) 0.1. x 10 8.) x 10 9.).6. x 10 11

3 Section 7. A. Writing Expressions with Exponents Simplify. Express each in exponential form: 1.) xxx x.) Algebra 1 Chapter 7 Notes.) aaabbbb.) x x x x.) y y y y 6.) m m m What pattern did you notice with the exponents? B. Multiplying Monomials Multiplying Monomials When I multiply variable expressions together, I the coefficients AND I the exponents of terms with the same base. Simplify each expression. Leave answers with positive exponents. 7.) (-m - n )(mn ) 8.) (-p q)(-p q -6 ) 9.) (9x - y z)(-x - yz) 10.) ) - 1.) (c 6 )(c - d 8 )(-cd - ) C. Applications to Scientific Notation Multiplying Numbers in Scientific Notation Multiply Coefficients (decimal terms) Add Exponents Check to make sure that the answer is in scientific notation 1.) (. x 10 )(.0 x 10 8 ) 1.) (1.6 x 10 - )(.0 x 10 ) 1.) (. x 10 - )(6. x 10-6 ) 16.) (9. x 10 - )(.1 x 10 ) 17.) (8. x 10-7 )(.6 x 10 - ) 18.) (-7. x 10 - )(9.1 x 10 8 )

4 D. Other Applications Complete each equation (fill-in-the-blank with a number) 17.) 18.) Algebra 1 Chapter 7 Notes 19.) 0.) x y ( ) x ( ) = y E. Comparing Addition and Multiplication 1.) (x )(x ) vs. x + x.) (7y )(y ) vs. 7y + y.) (1b )(b ) vs. 1b + b.) (7n )(n ) vs. 7n + n

5 Notes #: Review of Sections , Section 7. Algebra 1 Chapter 7 Notes Review of Sections ) Simplify: 7x -.) Simplify: -.) Evaluate x - if x = -.) Simplify: 1x x.) Evaluate for a = and b = - 6a b b 0 6.) Convert to scientific notation: 0, ) Convert to scientific notation: ) Convert to standard notation: 9.) Convert to scientific 6. x 10 8 notation: 7 x ) Simplify: (x y )(-x y ) 11.) Simplify each: (9m )(m ) vs. 9m + m 1.) Multiply; leave in scientific notation: (-. x 10-7 )(8.1 x 10 1 ) Section 7. A. Raising a Power to a Power Explore: 1.) (x ) versus (x )(x ).) (y ) versus (y ) Raising a Power to a Power Raise the coefficient to the power; evaluate the exponents on the variables Simplify; leave in terms of positive exponents:.) (x ).) (m ) (m ).) (g - ) - (g ) 6.) (w - )

6 7.) (d ) - 8.) (x y ) (xy ) 9.) (p - ) (p -10 ) 10.) (.) (.) - 11.) (a b - ) (ab ) 1.) ( ) ( - ) 1.) (x - )(xy ) Complete each equation (fill-in-the-blank with a number) 1.) (m ) = m 1 1.) m m = m 1 16.) (a b ) 1 = 6 1 ab B. Applications to Scientific Notation Raise the coefficient to the given power Multiply the exponents Check to make sure that your answer is in scientific notation Simplify. Write each answer in scientific notation 17.) (1. x 10 ) 18.) ( x 10-9 ) - 19.) (- x 10 ) 0.) (8 x 10 - ) Simplify. Leave your answer in scientific notation. 1.) (.6 x 10 )(6. x 10 7 ).) (. x 10 6 ).) (. x 10 8 )(1. x 10 ).) (. x 10 - ).) (6. x 10 7 ) 6.) (. x 10 8 )(1. x 10 ) 6

7 Combine like terms: 7.) 7m n + 6n 8m 8.) x 7x + 8x x 9.) ab ab + ab + 8ab 0.) 6j k 7j k + 8jk jk 1.) 19w 8 z 8w 7 z + 11w 8 z.) 10x y z x y z + x y z 7

8 Notes #: Review and Section 7. Review: Combine like terms. Distribute/Multiply first if necessary. 1.) x xx x.) y 6yy y9 y.) x(x ) + x(8 x).) -7x (6x ) + x(8 x ).) x(x y) x(y 7x) 6.) (x ) (x )(6x ) 7.) (a )(-a ) + (a )(a ) + (a ) (a ) Review Topics: 8.) Multiply; leave in scientific notation: (8. x 10 8 )(6.1 x 10 - ) 9.) Evaluate; leave in scientific notation: (. x 10 ) 10.) Simplify: (a b 6 )(-a b -9 ) 11.) Simplify: (w z 8 ) (-wz ) 1.) Simplify: 6mn m n 1 1.) Simplify each: (-b 6 )(b 6 ) vs. -b 6 + b 6 Section 7.: Division Properties of Exponents A. Dividing Monomials Explore: 6 a 1.) a.) x y x y.) 7 8

9 Dividing Monomials **When I divide like numbers or variables, I their exponents.** m a mn a n a Use this property to simplify the expressions. Leave all answers in positive exponents. 6 7 g 6 x 7 m.).) 6.) 6 g 6 x 7m 7.) c d cd ) xyz x yz 9.) 8 x y x z 6 8 z y 10.) 1 11.) x y z x y z 6 1.) m n B. Fractions to Negative Powers Explore: This is the same as: 1.) Fractions to Negative Powers **When I take a fraction to a negative power, I the fraction over, and raise it to the power. ** n n a b b a 1.) 1.) x 16.) w y 9

10 C. Applications to Scientific Notation Dividing Numbers in Scientific Notation Divide Coefficients (decimal terms) Subtract Exponents Check to make sure that the answer is in scientific notation 17.).8 x x ) 6.0 x x ) 1. x 10.0 x x 10. x 10 0.) 1.). x 10.1 x 10 10

11 Notes #: Chapter 7 Review Evaluate: Algebra 1 Chapter 7 Notes 1.).) -.) (-).) -(6x) 0.) ) 6 x y x y 0 7.) (-a - b 7 ) (-a b - ) 8.) (t 6 ) 1 9.) 8mn 7 1mn 8 10.) (-b c )(-b c)(b c) 11.) (-w - ) - (6w ) Write in standard notation: 1.) -.60 x 10-1.) 7.01 x 10 7 Write in scientific notation 1.) ) 8,900, ) ( x 10 )(0. x 10 - ) 17.) (.0 x 10 ) 18.) 1. x 10.0 x 10 7 Simplify: 19.) 0.) 8 1 xy xz 6 8 z y 11

12 Algebra 1: Chapter 7 Study Guide (HW#) Name: For #1-8, simplify each expression: 1.) (-) 0.) () -.) ) 0.) (7m ) 0 6.) (f) - 7.) - w x - y - 8.) ab c 1 For #9-11, evaluate each expression for m = - and n = 9.) m - n 10.) - m n - 11.) m -n For #1-1, write each number in scientific notation: 1.) ) 10,000 1.) 0.00 For #1-17, write each number in standard notation: 1.). x ).7 x ) 8 x 10 - For #18-0, is each number written in scientific notation? If not, convert to scientific notation. 18.) x ) 0. x 10-0.). x 10 - For #1-, rewrite each expression using the base only once 1.) ( )( )( - ) 8.).) (9.7) -8 (9.7) 8 1

13 For #-, simplify each expression. If applicable, leave your answer in scientific notation..) (bc 8 )(-b c)(b c - ).) (8. x 10 7 )(-1. x 10 - ) 6.) (d ) (d ) 7.) (-m - n ) 8.) ( x 10 ) 9.) (-x y ) (-8xy ) 0.) 7mn 9 mn 7 1.) xy 9xz z y.) t r 1.).6 x 10.) 1. x 10. x 10 7 x 10 6.) jk j k For #6-9, complete each equation (fill in the blank). _ 6.) ) x x 6x _ 7 8.) ab a a b 9.) _ **Please go online to correct your work in pen and print Chp 8 Notes!!** 1

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