# Chapter 7: Exponents

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1 Chapter : Exponents Algebra Chapter Notes Name: Notes #: Sections.. Section.: Review Simplify; leave all answers in positive exponents:.) m -.) y -.) m 0.) -.) -.) - -.) (m ) 0.) 0 x y Evaluate if a = - and b = -: 9.) a b - 0.) ab -.) a - + b -.) (ab) - Section.: Scientific Notation A. Why Scientific Notation? Compare:,000,000 vs. x vs. x 0 - Why do we use scientific notation? When will it be used most often? B. Format for Scientific Notation A number in scientific notation is written as the product of two factors in the form a x 0 n, where n is an integer and a 0 Examples: -. x x 0 GOAL:. x 0 Is each number written in scientific notation? If no, explain..) x 0.) -.90 x 0.) - x 0 0.

2 C. Writing in Standard Notation Converting from Scientific Notation to Standard Notation Algebra Chapter Notes If 0 is to a power, move the decimal that many places to the If 0 is to a power, move the decimal that many places to the Write in standard notation:.). x 0.) -. x 0 -.) 9. x 0 -.) -. x 0 D. Writing in Scientific Notation Converting from Standard Notation to Scientific Notation Place the decimal point so that you have digit to the left of the decimal point. Count the number of places you need to move the decimal to get back to your original number. This number will be the exponent on the 0. If you are moving to the left, this exponent will be If you are moving to the right, this exponent will be Write in scientific notation:.) - 9.),000 0.) 0.00.) -0.0.). x 0.) 0.0 x 0 -.).0 x 0 -.) x 0.) (. x 0 9 ).) (. x 0 ).) 0.(. x 0-9 ) 9.) 0.(. x 0 ) 0.).(. x 0 - ).).(0.0000).).(-. x 0 ).) (,000)()

3 Algebra Chapter Notes Order the numbers from least to greatest:.) 0.0 x 0,. x 0,. x 0 and.) 0. x 0 -, x 0, 0.0 x 0, x 0 - Section. A. Writing Expressions with Exponents Simplify. Express each in exponential form:.) x x x x.).) a a a b b b b.) x x x x.) y y y y.) 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..) (-m - n )(mn ).) (-p q)(-p q - ) 9.) (9x - y z)(-x - yz) 0.) -.) -.) (c )(c - d )(-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.) (. x 0 )(.0 x 0 ).) (. x 0 - )(.0 x 0 )

4 .) (. x 0 - )(. x 0 - ).) (9. x 0 - )(. x 0 ) Algebra Chapter Notes.) (. x 0 - )(. x 0 - ).) (-. x 0 - )(9. x 0 ) D. Other Applications Complete each equation (fill-in-the-blank with a number).).) 0 9.) x x 9x 0.) x y ( ) x ( ) = y E. Comparing Addition and Multiplication.) (x )(x ) vs. x + x.) (y )(y ) vs. y + y.) (b )(b ) vs. b + b.) (n )(n ) vs. n + n

5 Notes #: Review of Sections.-., Section. Algebra Chapter Notes Review of Sections.-..) Simplify: x -.) Simplify: -.) Evaluate x - if x = -.) Simplify: x x.) Evaluate for a = and b = - a b b 0.) Convert to scientific notation: 0, 000.) Convert to scientific notation: 0.0.) Convert to standard notation:. x 0 9.) Convert to scientific notation: x 0 0.) Simplify: (x y )(-x y ).) Simplify each: (9m )(m ) vs. 9m + m.) Multiply; leave in scientific notation: (-. x 0 - )(. x 0 ) Section. A. Raising a Power to a Power Explore:.) (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 ).) (w - ).) (d ) -.) (x y ) (xy ) 9.) (p - ) (p -0 ) 0.) (.) (.) -

6 Algebra Chapter Notes.) (a b - ) (ab ).) ( ) ( - ).) (x - )(xy ) Complete each equation (fill-in-the-blank with a number).) (m ) = m.) m m = m.) (a b ) = 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.) (. x 0 ).) ( x 0-9 ) - 9.) (- x 0 ) 0.) ( x 0 - ) Simplify. Leave your answer in scientific notation..) (. x 0 )(. x 0 ).) (. x 0 ).) (. x 0 )(. x 0 ).) (. x 0 - ).) (. x 0 ).) (. x 0 )(. x 0 ) Combine like terms:.) m n + n m.) x x + x x 9.) ab ab + ab + ab 0.) j k j k + jk jk.) 9w z w z + w z.) 0x y z x y z + x y z

7 Review Topics:.) Multiply. Leave your answer in scientific notation:. x 0. x 0.) Find f(-) if f(x) = x Algebra Chapter Notes.) Are the lines parallel, perpendicular, or neither? y x x y.) Find the x-intercept and the y-intercept of the line: x y = 0.) Solve: x.) Solve for x and y: x y x y.) Graph the linear inequality: x y 0 y 0 9 x

8 Notes #: Review and Section. Review: Algebra Chapter Notes Combine like terms. Distribute/Multiply first if necessary..) x x x x.) y y y y 9 y.) x(x ) + x( x).) -x (x ) + x( x ).) x(x y) x(y x).) (x ) (x )(x ).) (a )(-a ) + (a )(a ) + (a ) (a ) Review Topics:.) Multiply; leave in scientific notation: (. x 0 )(. x 0 - ) 9.) Evaluate; leave in scientific notation: (. x 0 ) 0.) Simplify: (a b )(-a b -9 ).) Simplify: (w z ) (-wz ).) Simplify: mn m n.) Simplify each: (-b )(b ) vs. -b + b Section.: Division Properties of Exponents A. Dividing Monomials Explore: a.) a.) xy xy.)

9 Algebra Chapter Notes Dividing Monomials **When I divide like numbers or variables, I their exponents.** m a m n a n a Use this property to simplify the expressions. Leave all answers in positive exponents. g x m.).).) g x m.) c d cd 9.) x y z x y z 9.) x y x z z y 0.).) x y z x y z.) m n B. Fractions to Negative Powers Explore: This is the same as:.) Fractions to Negative Powers **When I take a fraction to a negative power, I the fraction over, and raise it to the power. **.) a b.) n b a x n.) w y 9

10 Algebra Chapter Notes 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.). x 0. x 0.). x 0.0 x 0 9.). x 0.0 x ).9 x 0. x 0.). x 0. x 0 Review Topics:.) Solve for x and y: x y y x.) Solve for x and y: x y x y.) Graph the line: x y = - y 0 9 x ) Find the equation of the line with slope and passing through the point (-, ). Leave your answer in slope intercept form. 0

11 Notes #: Chapter Review Evaluate: Algebra Chapter Notes.).) -.) (-).) -(x) 0.) - -.) xy xy 0.) (-a - b ) (-a b - ).) (t ) 9.) mn mn 0.) (-b c )(-b c)(b c).) (-w - ) - (w ) Write in standard notation:.) -.0 x 0 -.).0 x 0 Write in scientific notation.) 0.00.),900,000.) ( x 0 )(0. x 0 - ).) (.0 x 0 ).). x 0.0 x 0 Simplify: 9.) 0.) x y x z z y

12 Review Topics:.) Divide. Leave your answer in scientific notation:. x 0.0 x 0.) Find h(-) if h(x) = x Algebra Chapter Notes.) Does the system have no solution, one solution, or infinitely many solutions? y x x y.) Simplify: m 0m m 0m.) Find the equation of the line with slope ½ and passing through the point (-, ).) Find the equation of the line passing through the points (, 0) and (, 0)..) Simplify: (x y).) Find g(-) if g(x) = x

13 Algebra Chapter Notes 9.) Find the slope and y-intercept of each line. What can you conclude? 0.) Graph: x y x y x y y ) Find the equation of the line that is parallel to y = -x + and passing through the point (, ).) Find the equation of the line that is perpendicular to y = -x + and passing through the point (, )

14 Algebra Chapter Notes Algebra : Chapter Study Guide Name: For #-, simplify each expression:.) (-) 0.) () -.) - -.) 0.) (m ) 0.) (f) -.) - w x - y -.) ab c For #9-, evaluate each expression for m = - and n = 9.) m - n 0.) - m n -.) m -n For #-, write each number in scientific notation:.) 0.00.) 0,000.) 0.00 For #-, write each number in standard notation:.). x 0 -.). x 0.) x 0 - For #-0, is each number written in scientific notation? If not, convert to scientific notation..) x 0 9.) 0. x 0-0.). x 0 - For #-, rewrite each expression using the base only once.) ( )( )( - ).).) (9.) - (9.)

15 Algebra Chapter Notes For #-, simplify each expression. If applicable, leave your answer in scientific notation..) (bc )(-b c)(b c - ).) (. x 0 )(-. x 0 - ).) (d ) (d ).) (-m - n ).) ( x 0 ) 9.) (-x y ) (-xy ) 0.) mn 9 mn.) xy 9xz z y.) t r.). x 0. x 0.). x 0 x 0.) jk j k For #-9, complete each equation (fill in the blank)..).) x x x.) ab a a b 9.) _

16 Algebra Chapter Notes 0.) Simplify: m m m m.) Simplify: x(xy y ) y x x.) Find the slope of the line passing through the points: (-, ) and (, -).) Find the equation of the line with slope of that passes through the point (9, -). Leave in slope-intercept form..) Graph the line: x y = -.) Solve for x: y 0 9 x ) Solve for x and y: x y x y x.) Solve for x: x.) Find g(-) if g(x) = x 9.) Are the lines parallel, perpendicular, or neither? y x x y 0.) Find the x-intercept and the y-intercept of the line: x y 9

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