Chapter 7: Exponents

Transcription

1 Chapter : Exponents Algebra Chapter Notes Name: Algebra Homework: Chapter (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework M / Review of Sections.-. Section.: Raising a Power to a Power Combine Like Terms HW# Pg. : -0 even Pg. : -0 even Pg. : - even T /9 Section.: Division Properties of Exponents Multiply and combine like terms HW# Pg. : - all, - even (SKIP 0) Pg. : - even Pg. : -9 odd Chapter Test and Notes Check on Thursday / W /0 Chapter Review HW# Study Guide Correct Study Guide Online Chapter Test and Notes Check on Thursday / Th / Chapter Test HW# Pg. : - odd Pg. : -0 even Print: Chapter Notes

2 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: 9.) Convert to scientific. x 0 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.) (.) (.) -

3 .) (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

4 Review Topics:.) Multiply. Leave your answer in scientific notation:.) Find f(-) if f(x) = x. x 0. x 0 Algebra Chapter Notes.) Are the lines parallel, perpendicular, or neither? y x xy.) 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: xy 0 y x

5 Notes #: Review and Section. Review: Combine like terms. Distribute/Multiply first if necessary..) x xx x.) y yy y9 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.) x y x y.)

6 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. g x m.).).) g x m.) c d cd 9.) xyz x yz 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. ** n n a b b a.).) x.) w y

7 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.).0 x 0 0. x 0 9.). x 0.0 x 0.9 x 0. x 0 0.).). x 0. x 0 Review Topics:.) Solve for x and y: xy y x.) Solve for x and y: x y x y.) Graph the line: x y = - y x ) Find the equation of the line with slope and passing through the point (-, ). Leave your answer in slope intercept form.

8 Notes #: Chapter Review Evaluate: Algebra Chapter Notes.).) -.) (-).) -(x) 0.) - -.) x y x y 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.) xy xz z y

9 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 xy.) 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 9

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

11 Algebra : Chapter Study Guide (HW#) 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.)

12 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.) _

13 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 = - y x ) Solve for x and y: x y x y.) Solve for x: 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