3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.

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1 SECTION. Eponents nd Rdicls 7 B NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd the numer 4 is clled the.. () When we multiply two powers with the sme se, we the eponents. So When we divide two powers with the sme se, we the eponents. So. 3. () Using eponentil nottion, we cn write 3 s. Using rdicls, we cn write / s. Is there difference etween nd? Eplin. 4. Eplin wht 4 3/ mens, then clculte 4 3/ in two different wys: 4 / or 4 3. Eplin how we rtionlize denomintor, then complete the following steps to rtionlize : Find the missing power in the following clcultion: /3. SKILLS 7 4 Write ech rdicl epression using eponents, nd ech eponentil epression using rdicls Rdicl epression Eponentil epression 9. 4 /3 0. 3/ Rdicl epression Eponentil epression 3. / 4. 4 Evlute ech epression.. () 3 3 A 3B () () A 3B 0 A 4B 8. () A 3 B 9 A 3B 3 9. () () () () () A 4 9B / 3 / 4. () Evlute the epression using 3, y 4, nd z.. y y z 7. 9 /3 y /3 z /3 8. y z 9 34 Simplify the epression y 4 3 y 3 40 Simplify ech epression. 3. () 6 8 3y 4y 36. () z z 3 z 4 y 0 y () y 7 3 A 7 8 B /3 0 A 4 A / A 64B 3/ z z () y 3 8 z 3 z Copyright 00 Cengge Lerning. All Rights Reserved. My not e copied, scnned, or duplicted, in whole or in prt. Due to electronic rights, some third prty content my e suppressed from the ebook nd/or echpter(s). Editoril review hs deemed tht ny suppressed content does not mterilly ffect the overll lerning eperience. Cengge Lerning reserves the right to remove dditionl content t ny time if susequent rights restrictions require it.

2 CHAPTER Fundmentls 39. () z 6z () z z Simplify the epression nd eliminte ny negtive eponents(s). 4. () 4 y 4 y 8 za 3 z 4 B 4. () () y 3 3 y () s t s t 3 u 3 3 3u 3 6y 3 z y z () yz y z 3 3 y () y 3 3 u 47. () 3 3 c 3 u 3 3 rs () 4 z 3 4y y z 3 r 3 s 49. () y y 0. () y 3. () 3 3. () s t 4 s t 3 60 Simplify the epression. Assume tht the letters denote ny rel numers y y z 6 70 Simplify the epression nd eliminte ny negtive eponent(s). Assume tht ll letters denote positive numers. 6. () 3/4 /4 6. () 4 / 8 /4 3 3/4 / 4/3 /3 s / s /4 63. () /3 3 3 q r s r sq 8 y z 3 y 3 z y /3 y 4/3 s / 64. () u4 6 /3 8y 3 /3 6. () 8 6 3/ / / 66. () y /3 3/ 3 y /4 8y 3/ /3 67. () 8s 3 t 3 /3 3y z 0 / s 4 t 8 /4 64y 6 z /6 68. () 8 y 4 /4 8y3/4 6y 4/3 y 3 z 6 / s3 t A4s 7 tb6t () /3 /6 y 3 y / 70. () /6 3 3 y 3/ y / Simplify the epression nd eliminte ny negtive eponents(s). Assume tht ll letters denote positive numers. 7. () 6 y 3 y 7. () () 4st 3 6 s 3 t () 3 y 0 4 y 6 7. () 3 yy 76. () 3ss Write ech numer in scientific nottion. 77. () 69,300,000 7,00,000,000, (d) () 9,40,000 7,9,000, (d) Write ech numer in deciml nottion. 79. () (d) () (d) Write the numer indicted in ech sttement in scientific nottion. 8. () A light-yer, the distnce tht light trvels in one yer, is out,900,000,000,000 mi. The dimeter of n electron is out cm. A drop of wter contins more thn 33 illion illion molecules. 8. () The distnce from the erth to the sun is out 93 million miles. The mss of n oygen molecule is out g. The mss of the erth is out,970,000,000,000,000,000,000,000 kg Use scientific nottion, the Lws of Eponents, nd clcultor to perform the indicted opertions. Stte your nswer rounded to the numer of significnt digits indicted y the given dt y3 z /3 3 y 6 /3 / 8z 4 9st 3/ 3s 7s 3 t 4 /3 4t /3 4 6u 3 B u 3 4 y 4 B y Copyright 00 Cengge Lerning. All Rights Reserved. My not e copied, scnned, or duplicted, in whole or in prt. Due to electronic rights, some third prty content my e suppressed from the ebook nd/or echpter(s). Editoril review hs deemed tht ny suppressed content does not mterilly ffect the overll lerning eperience. Cengge Lerning reserves the right to remove dditionl content t ny time if susequent rights restrictions require it.

3 SECTION. Eponents nd Rdicls ,6, Rtionlize the denomintor. 89. () 0 B y 90. () B B 6 B z 9. () 4 y 3 9. () Let,, nd c e rel numers with 0, 0, nd c 0. Determine the sign of ech epression. () 0 c 3 (d) 3 (e) 4 (f) 94. Prove the given Lws of Eponents for the cse in which m nd n re positive integers nd m n. () Lw Lw Lw 6 APPLICATIONS B 3 3 c 3 6 c 6 9. Distnce to the Nerest Str Proim Centuri, the str nerest to our solr system, is 4.3 light-yers wy. Use the informtion in Eercise 8() to epress this distnce in miles. 96. Speed of Light The speed of light is out 86,000 mi/s. Use the informtion in Eercise 8() to find how long it tkes for light ry from the sun to rech the erth. 97. Volume of the Ocens The verge ocen depth is m, nd the re of the ocens is m. Wht is the totl volume of the ocen in liters? (One cuic meter contins 000 liters.) y / c 3/7 98. Ntionl Det As of July 00, the popultion of the United Sttes ws ,nd the ntionl det ws dollrs. How much ws ech person s shre of the det? 99. Numer of Molecules A seled room in hospitl, mesuring m wide, 0 m long, nd 3 m high, is filled with pure oygen. One cuic meter contins 000 L, nd.4 L of ny gs contins molecules (Avogdro s numer). How mny molecules of oygen re there in the room? 00. How Fr Cn You See? Becuse of the curvture of the erth, the mimum distnce D tht you cn see from the top of tll uilding of height h is estimted y the formul where r 3960 mi is the rdius of the erth nd D nd h re lso mesured in miles. How fr cn you see from the oservtion deck of the Toronto CN Tower, 3 ft ove the ground? CN Tower D rh h 0. Speed of Skidding Cr Police use the formul s 30fd to estimte the speed s (in mi/h) t which cr is trveling if it skids d feet fter the rkes re pplied suddenly. The numer f is the coefficient of friction of the rod, which is mesure of the slipperiness of the rod. The tle gives some typicl estimtes for f. () If cr skids 6 ft on wet concrete, how fst ws it moving when the rkes were pplied? If cr is trveling t 0 mi/h, how fr will it skid on wet tr? r Tr Concrete Grvel Dry Wet Copyright 00 Cengge Lerning. All Rights Reserved. My not e copied, scnned, or duplicted, in whole or in prt. Due to electronic rights, some third prty content my e suppressed from the ebook nd/or echpter(s). Editoril review hs deemed tht ny suppressed content does not mterilly ffect the overll lerning eperience. Cengge Lerning reserves the right to remove dditionl content t ny time if susequent rights restrictions require it.

4 4 CHAPTER Fundmentls 0. Distnce from the Erth to the Sun It follows from Kepler s Third Lw of plnetry motion tht the verge distnce from plnet to the sun (in meters) is d GM 4p /3 T /3 where M kg is the mss of the sun, G N m /kg is the grvittionl constnt, nd T is the period of the plnet s orit (in seconds). Use the fct tht the period of the erth s orit is out 36. dys to find the distnce from the erth to the sun. DISCOVERY DISCUSSION WRITING 03. How Big Is Billion? If you hd million (0 6 )dollrs in suitcse, nd you spent thousnd (0 3 ) dollrs ech dy, how mny yers would it tke you to use ll the money? Spending t the sme rte, how mny yers would it tke you to empty suitcse filled with illion (0 9 ) dollrs? 04. Esy Powers Tht Look Hrd Clculte these epressions in your hed. Use the Lws of Eponents to help you. 8 () Limiting Behvior of Powers Complete the following tles. Wht hppens to the nth root of s n gets lrge? Wht out the nth root of? n /n 0 00 Construct similr tle for n /n. Wht hppens to the nth root of n s n gets lrge? 06. Compring Roots Without using clcultor, determine which numer is lrger in ech pir. () / or /3 A B / or A B /3 7 /4 or 4 /3 (d) 3 or 3 n 0 00 A B /n.3 ALGEBRAIC EXPRESSIONS Adding nd Sutrcting Polynomils Multiplying Algeric Epressions Specil Product Formuls Fctoring Common Fctors Fctoring Trinomils Specil Fctoring Formuls Fctoring y Grouping Terms A vrile is letter tht cn represent ny numer from given set of numers. If we strt with vriles, such s, y, nd z nd some rel numers, nd comine them using ddition, sutrction, multipliction, division, powers, nd roots, we otin n lgeric epression. Here re some emples: y z y 4 A monomil is n epression of the form k,where is rel numer nd k is nonnegtive integer. A inomil is sum of two monomils nd trinomil is sum of three monomils. In generl, sum of monomils is clled polynomil. For emple, the first epression listed ove is polynomil, ut the other two re not. POLYNOMIALS A polynomil in the vrile is n epression of the form n n n n... 0 where 0,,..., n re rel numers, nd n is nonnegtive integer. If n 0, then the polynomil hs degree n. The monomils k k tht mke up the polynomil re clled the terms of the polynomil. Note tht the degree of polynomil is the highest power of the vrile tht ppers in the polynomil. Copyright 00 Cengge Lerning. All Rights Reserved. My not e copied, scnned, or duplicted, in whole or in prt. Due to electronic rights, some third prty content my e suppressed from the ebook nd/or echpter(s). Editoril review hs deemed tht ny suppressed content does not mterilly ffect the overll lerning eperience. Cengge Lerning reserves the right to remove dditionl content t ny time if susequent rights restrictions require it.

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