1.1 Reviewing the Exponent Laws

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1 . Reviewing the Exponent Lws INVESTIGATE & INQUIRE An order of gnitude is n pproxite size of quntity, expressed s power of 0. The tble shows soe speeds in etres per second, expressed to the nerest order of gnitude. Entity Light (in spce) Sound (in ir) Horse (glloping) Hun (wlking) Grden snil. Express 0 0 etres per second in stndrd for.. Use division to deterine, to the nerest order of gnitude, how ny ties s fst ) light is s sound b) horse is s snil. Write the rule you used to divide two powers of 0.. To the nerest order of gnitude, the oon orbits the Erth 0 6 ties s fst s snil cn trvel. Use ultipliction to express the speed of the oon in etres per second, to the nerest order of gnitude. 5. Write the rule you used to ultiply two powers of 0. The following sury shows the exponent lws for integrl exponents. Exponent Lw for Multipliction ( )( ) 6 MHR Chpter Speed (/s) n ( )( ) n fctors + n fctors + n

2 Exponent Lw for Division Power Lw (5 ) (5 5) (5 5)(5 5)(5 5) Power of Product (5 ) (5 ) (5 ) (5 ) Power of Quotient n, 0 n fctors n fctors n ( ) n ( ) n ( ) ( ) ( ) n fctors n n ties (b) (b) (b) (b) ( ) (b b b) b b b b b b b b, b 0 b. Reviewing the Exponent Lws MHR 5

3 A power is n expression in the for. The exponent lws cn be used to siplify expressions with powers. EXAMPLE Siplifying Expressions With Powers Siplify. ) ( b)( b ) b) ( ) c) ( p q ) SOLUTION ) ( b)( b ) ( ) b b 6 5 b b) ( ) c) ( p q ) ( ) (p ) (q ) 6p 9 q 6 EXAMPLE Siplifying Power of Quotient Siplify 6x 5 y. 8y SOLUTION Use the power of quotient lw first. 6x 5 y (6) (x 5 ) (y ) 8y (8) (y ) 6x 0 y 6 6y 8 9x 0 6y SOLUTION Siplify the quotient first. 6x 5 y x 5 8y y () (x 5 ) () (y) 9x0 6y 6 MHR Chpter

4 The following surizes the rules for zero nd negtive exponents. Zero Exponent 0 but so 0 0 but Negtive Exponents + ( ) 0 so Divide both sides by. so, if 0, 0 Note tht 0 0 is not defined. + ( ) 0 so Divide both sides by. so, if 0, EXAMPLE Siplifying Expressions With Negtive Exponents ( 6x y)( 9x 5 y ) Siplify. Express the nswer with x y SOLUTION ( 6x y)( 9x 5 y ) x y 5x 7 y Multiply: x y Divide: 8x 9 y Rewrite: 8y x 9 Siilrly, if 0, EXAMPLE Evluting Expressions With Zero nd Negtive Exponents Evlute. ) ( 6) 0 b) c) + 6. Reviewing the Exponent Lws MHR 7

5 SOLUTION Pper-nd-Pencil Method ) ( 6) b) c) SOLUTION Grphing-Clcultor Method The first nswer given by grphing clcultor y be decil. If necessry, convert the decil to frction using the Frc function. ) b) c) 5 8 Key Concepts Exponent lw for ultipliction: n + n Exponent lw for division: n n Power lw: ( ) n n Power of product lw: (b) b Power of quotient lw: b b Zero exponent property: if 0, 0 Negtive exponent property: if 0, nd 8 MHR Chpter

6 Counicte Your Understnding. Describe how you would siplify ( x y )(xy ).. Describe how you would evlute using pper nd pencil. +. Wht is the vlue of 0? Explin.. Explin why 0 for the negtive exponent property. Prctise A. Express s power of. ) b) 6 c) ( ) d) 7 e) f) 7 y g) x h) ( x ) y i) j) 5 k) ( ) l) 0. Evlute. ) b) 5 0 c) ( ) d) ( ) e) ( ) 0 f) g) h) ( ) ( ) 5. Siplify. Express ech nswer with ) b) ( 6 )( ) c) b 5 b 6 b d) b e) (x )(y)(y )(x 5 ) f) (x )(x 5 ) g) 5 h) y y y i) 5 0 j) ( )(b )( ). Siplify. Express ech nswer with ) x 6 x b) 7 c) t t d) y 5 y e) 0 f) t 0 t 5 5. Siplify. Express ech nswer with ) (x ) b) ( b ) c) (x ) d) (t ) 0 e) ( b ) f) (x y ) 6. Siplify. Express ech nswer with x ) x b) c) b y x d) e) b 5 7. Siplify. Express ech nswer with ) 5 b) (b )( 5 b ) c) 5( b )( b ) d) ( 6 n )( n 5 ) e) (7x )(6x ) f) (x y )( x y ) g) ( 6 b )( b ) h) ( 0x ) ( x) 5 b ( n )(7 n) i) j) 9b n 5 k) b 0 b b l) 5 b 6 5 b 6 (b ) ) (5x 5 ) (5x ) n) 5 5 b 7 6 b o) ( 6 n ) ( n 6 ) ( x y)( x y ) p) 6xy 8. Siplify. Express ech nswer with ) ( ) b) ( x ) c) ( n ) d) (5c d ) e) ( b ) f) ( x y ). Reviewing the Exponent Lws MHR 9

7 x y n y g) h) i) 6b b b x y 8x y j) k) l) 9. Evlute. 6 ) b) c) + x 0 + y 0 n 0 + d) e) 5 (6 + 6 ) 0 Apply, Solve, Counicte Web Connection 0. History The Burgess Shle in British To lern ore bout the fossils in the Burgess Colubi s Yoho Ntionl Prk contins Shle, visit the bove web site. Go to Mth one of the world s best fossil collections. Resources, then to MATHEMATICS, to find The fossils re bout yers old. out where to go next. Describe why fossils in the This is bout.5 0 ties s old s the first Burgess Shle re so well preserved. known hun settleent in British Colubi. About how ny yers go did huns first settle in British Colubi? B. Appliction A piece of wood burns copletely in one second t 600 C. The tie the wood tkes to burn is doubled for every 0 C drop in teperture nd hlved for every 0 C increse in teperture. In how ny seconds would the wood burn t ) 500 C? b) 650 C?. Inquiry/Proble Solving Use brckets to ke ech stteent true. Justify your solution. ) b) 0. Without evluting the expressions, deterine which is greter, 0 00 or C. Evlute ) b) c) n ( n + n ) d) x x Couniction ) For which non-zero rel vlues of x is x ( x)? Explin. b) For which non-zero rel vlues of x is x ( x)? Explin. 6. Equtions Deterine the vlue of x. ) x x b) x 5 x 6 c) x x d) x x For which vlues of x is x x true? Explin. 0 MHR Chpter

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