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1) 2 − 2 =125273)   =  7 21<1;4=2−52) (0,013) −1 =  13  1000 35 π7)   45−218)   38−3274. 1) a3) (b75. 1)39= 2−31> 0;2< 1 = 2 0 , так как − 3 < 0 ;2− 5 4=  π2− 5 4; 1 < 4 ; 5 > 4 = 2; значит, 2 − 5 < 0, а  π π= 33− 8 ; 3 = 9 > 8 , значит, 3 − 8 > 0, то есть 33−⋅ a1−3)321000= 76 > 1 ;1313< 1 = 2 0 , так как − 5 < 0 ;36)  1 2== (3,5) −5 < 1 = (3,5) 0 , так как −5 < 0 ;4) 271,5 = (33 ) 2 = 32 > 1 = 30 , так как 4−5) 2−12=a2:b = b2 +1− 2= a1 = a ;3⋅ 3−213⋅b3= b ⋅b−2=b132 = 2 < 3 3 = 3 , так как 3>2; 2)176. 1)   16 −0,753 −12) a3− 24⋅a3 +1=a80 4<1=   ; π> 1 = 30 .3 −1+ 3 +1= a2=b =b.115 = 5 4 < 4 7 = 7 4 , так как 7>5.113 35  53 224 + 19  54 43− = (2 ) + 30 −  5  = 2 + 30 − = 8 + 30 − 1,5 = 36,5 ;2 32 2 −132) (0,001) − 2−223⋅ 64 − 81−13−1241 1 3−26 33 −33 3= − 2 ⋅ (2 ) − (2 ) = (10 ) – 1000 24www.5balls.ru;131 19  5+ 8100000,25 −  7  = (16) 4 + (304 ) 4 − 32 13− 2− 2 ⋅ 24 − 2− 4 = 10 − 24− 2 −233) 27 − (−2)1  33 =3 − + 34  2 −2−44) (−0,5)8 +1–  4 −12+12−2 3+ 3  813= 10 − 2 2 − 0,0625 = 9,9375 − 4 = 5,9375 ;1−1 3−1 24 + 3  3= (3 ) −+=2  8 (−2)23311 2 9 ⋅ 12 − 3 + 2 ⋅ 4 108 − 3 + 8 1135+ ====9 ;1212124 312=9−− 625124 1−2  40,251−12 1 =  −2 −41− (54 ) 4 −432 − 135 − 8 28919.== 10272727=−3−b42⋅6277.

1) (a 4 ) 4 ⋅ (b 3 ) −6 = a −3 ⋅ b 3 = a −3 ⋅ b 4 =1a3;1  a 6  4 12  a 6  312)   −3   =  −3  = (a 6 ⋅ b3 ) 3 = a 2 ⋅ b .b   b  4a 3 (a78. 1)14−1324+ a3)34−=1414a (a + a )1−1−14a ⋅ a (a144 1−32 1+a 3 ⋅ a 3 (1 + a 3 3 )1−3 1+4 41=+ 1)1−(1 + a ) =a3a1 1−4 4(a + 1)aa0=a=a;11 1−4 1+55b5 ( b4 − b−1) b5 (b5 − b 5 ) b5 ⋅ b 5 (b5 5 −1) −b ± b2 − 4ac b5 5 ( b −1) b0 12) 2= 2 1 2 = 2 2 12= 22= 0 = =1 ;−−+−2a13b3 (3 b − b−2 ) b3 (b3 − b 3 ) b3 ⋅ b 3 (b3 3 −1)b3 3 ( b −1) b53)2=−3 2a − b−21313a4)13a 3 b −1 − ab+b623=1a +b1a23=−1323121311(1a 3 b −1 a 2 − b5 1+a −ba +6b=23a −ba b +b a12=26362113a b + b6a 6a 6 + b623);2211a 6 b 6 (a 6 + b 6 )=1a 6 + b61=a 6 + b61a 6 b 6 (a 6 + b6 )16−−a 3 (a 3 3 ⋅ b −1 − 1)1652211= a 6b 6 = a 3b3 .1−51−1−1−661−1−79. 1) (23 ⋅ 3 3 − 33 ⋅ 2 3 ) ⋅ 3 6 = 3 3 ⋅ 2 3 (23 − 33 )3 6 = 6 3 ⋅ 6 3 (22 − 32 ) == 6 = 4 − 9 = −5 ;1331 3+4131−31−332) (5 4 : 2 4 − 2 4 : 5 4 ) 4 1000 = (5 4 ⋅ 2 4 − 2 4 ⋅ 5 4 ) ⋅ 10 4 =−3−= 2 4 ⋅ 5 4 (5 41 3+3−3−3− 2 4 4 ) ⋅ 10 4 = 10 4 ⋅ 10 4 (5 − 2) = 103 3− +4 4⋅ 3 = 100 ⋅ 3 = 1 ⋅ 3 = 3 .25www.5balls.ru1180.

1) a 9 6 a 3 a = a 9 ⋅11−41 2+9a = a 9 ⋅ a 6⋅3 = a 95134 52) b12 3 b 4 b = b12 ⋅3163 41b = b12 ⋅ b 3−4 = b12116−2−1−+1= a3 ;51211= b2 ;142−4−1−1143) ( ab−2 + (ab) 6 ) ab 4 = (a 3 b 3 + a 6 b 6 )a 6 b 6 = (a 6 b 6 + a 6 b 6 )a 6 b 6 =−1−433141 1−1 1−111111= a 6 b 6 (a 6 + b 6 )a 6 b 6 = a 6 6 b 6 6 (a 2 + b 2 ) = a 0b0 (a 2 + b 2 ) = a 2 + b 2 ;2211114) ( 3 a + 3 b)(a 3 + b 3 − 3 ab) = (a 2 + b 2 )(a 3 + b 3 ) ×111111×((a 3 )2 − a 3 b 3 + (b 3 )2 ) = (a 3 )3 + (b 3 )3 = a + b .111181. 1) (1 − 2 b + b ) : (a 2 − b 2 )2 = 1 (a − 2 ab + b) : (a 2 − b 2 )2 =aaa11= ( a − b )2 : ( a − b )2 = ;aa1111111 122−−a 3b+) = (a 3 + b 3 ) : (a 3 − b 3 ⋅ (2a 3 b 3 + a 3 + b 3 ) =ba2) (a 3 − b 3 ) : (2 + 31111111111= (a 3 + b 3 ) ⋅ a 3 ⋅ b 3 : : (a 3 + b 3 )2 = a 3 ⋅ b 3 : (a 3 + b 3 ) ;13)9a4 − a414−−54a −ab−123− b212b +b=1−2181444a 4 (1 − a 4 )−14b 2 (1 − b 2 )−1−2a (1 − a )22=b (b + 1)1 − a2−1− a2b − 1 (1 − a )(1 + a ) (1 − b)(1 + b)=−= 1+ a −1+ b = a + b ;1+ b1+ a1+ b−13−11−21−1−12a − a 2ba2 − a 3b a 2 − a 2b a 3 − a 3ba 2 (a 2 − b)4)−=− 1= 1 1−11 11 11−−−1 − a − 1b 6 a + a 3 b 1 − a 2 b 2 a 6 + a 3 b 2 a − 2 (a 2 − b 2 )−13a 3 (a 3 − b)−−13a−b=1111a 2 + b21−111=111(a 2 − b 2 )(a 2 + b 2 )1a 2 + b211−a 2 − b21111( mn )7232+ 37 +1⋅y( xy )a 2 + b217−b3==x(mn )(mn )732+ 3⋅y7( xy)7⋅y==(mn )32(mn ) (mn )( xy)( xy)7⋅y73=1(mn )2;= y;+ b 3 ) = ((a 2 )2 − (b 3 )2 ) = a 2 2 − b2 3 ;4) (2a −0,5 − 1 b− 3 )( 1 b− 3 + 2a −0,5 ) = (2a −0,5 )2 − (1 b− 3 )2 = 4a −1 − 1 b−293333) (a1(a 2 − b 2 )(a 2 + b 2 )−a 2 + b 2 = 2b 2 = 2 b .382.

1) m n2) x1a 2 − b2a 3 (a 6 − b 2 )1a−b−)(a226www.5balls.ru3.=83. 1) (a1+ 2 )1−= a (1+21− 52) (m 1+ 5 ) −3 ⋅ m3 522)(1− 2)3 5 −3 3 5+25= m 1+3) (a 32 + 3 3 3 4 −3 6 + 3 94) (a 39 + 3 3 +1 1− 3 3= a (1−3)6 5 −6+3 5 +3⋅52(1+ 5 )=m9= m 2 = m 4,5 ;8 −3 12 +3 18 +3 12 −3 18 +3 27= a3)= a1− 2 = a −1 ;1213 )( 3 3 +13⋅ 3 +1)23 +3 33= a3= a 2+3 = a5 ;13= a1− (33 )3= a −2 .84. 1) 52 x = 54 ; 2 x = 4; x = 2 ;2)  1 2x2−111=   ; 2 x = −1; x = − ;22 3) 9 x = 3 2x4) 16 = 285. 1) 7 x2) 25x2( 2)4) ( 3 )x3)3x28π; 32 x = 32; 24x=2= 7 ; 7x3= 5 5 ; 52x128π32; 2x = 2 2 ; x = 2 ;; 4 x = 8π; x = 2π .111; x=;22 31133;= 5 2 ; 2x 2 = ; x =24 2= 72 ; x 3 =x11x3x 3= ; x = 3;2 233x 3= ; x =1.= 32 ;22= 2 2; 22 = 2 2 ; 2 2 = 22 ;1= 3 3 ; 32⋅3x113x= 3 2; 3 286.

1) 3 10 = 15 10 5 = 15 100000 > 5 20 = 15 (20) 3 = 15 8000 ;2)45=12 35 = 12 125 < 3 7 =127 4 = 12 2401 ;3) 17 = 6 17 3 = 6 4913 > 3 28 = 6 28 2 = 6 784 ;4) 4 13 = 20 13 5 = 20 371293 > 5 23 = 20 23 4 = 20 279841 .33=13111111a 2 (b 2 − a 2 ) − ab 2 (b 2 + a 2 ) 2a 2a2ab 22a 2+=−−=b−aa −ba+ bb − a a−b87. 1)3 1+1+111 1+3131a 2 b 2 − a 2 2 − a 2 b 2 − ab 2 2 + 2a 2 a 2 b 2 − a 2 − a 2 b 2 − ab + 2a 2 a2 − ab a(a − b)==== −a ;b−ab−ab − a −(a − b)22) 3xy − y −x−yy yx− y−y x=x+ y3xy − y 2−x−y2−y xy + y + yx − y xy 3xy − y 2 − y 2 − xy 2xy − 2y 22(x − y)y== 2y ;==x−yx−yx−yx−y3)13a +3b−322a +3b2a 3 + 3 ab + b 322211a 3 − 3 ab + b 3 − a 3 − b 3 − 2a 3 b3 −33 ab;==a+ba+b27www.5balls.ru4)3 23a − b23a −3b−a −b2=2a 3 + 3 ab + b 31( 3 a − 3 b)( 3 a + 3 b)3−a −3b122(а 3 − b 3 )(a 3 + 3 ab + b 3 )22a 3 + 3 ab + b 3== 3 a + 3 b − 3 a + 3 b = 23 b .88.

1)a−b3−a −3b21113113=11+131112211+2211a 3 − b311=21131−2ba 3 ;= 22a 3 − b31(a + b ) (a 3 + b 3 ) − (a − b ) (a 3 − b 3 ) =a+ba 3 + a 3b3 + b 3131+1+ ab 3 − a 3 b − b 3 + ab 3 − ba 3 + ba−b−a 3 − a 3b3 + b 313aa 3 + b3a+b2)a+ba−b13= a + b − a + b = 2b ;222333) a + b −a−b111a 3 + b3221112a 3 − a 3b3 + b3x+y2111112112112x 3 + x 3 y3 + y 31x−y111313x −y3311111121111=112313311332a −b321=11a −b11+1=11111133=33228www.5balls.ru=(a 2 + b 2 )(a + a 2 b 2 + b)3131(a + b)(a 2 + b 2 )(a 2 − b 2 )12(a 2 + b 2 )(a 2 + b 2 )3211a2 + b2 − 2ab(a + b)(a + b − 2a 2 b2 )332(a 2 + b 2 − a 2 b 2 − a 2 b 2 )11a 2 − b2=1x+ya 2 − b2311( x + y ) (x 3 + y 3 ) +1a 2 + b 2 − 2ab + a 2 + b 2 + ab + ab − 2a 2 b 2 − 2a 2 b 23=1a 2 − b2a 2 − b211(a − b)2a 2 − b231121a2 + b2 − 2ab=11x 3 + y3 + x 3 − y3 − x 3 − y3 = x 3 − y3 ;(a + b ) (a 2 − b 2 )(a 2 − b 2 ) ==121(a 2 + b 2 )(a + a 2 b 2 + b)12x 3 − x 3 y3 + y 3a 2 − b2+a 2 − b22x 3 − y3−( x − y ) (x 3 − y 3 ) − (x 3 − y 3 )(x 3 + y 3 ) =+2)22x−y+x 3 − x 3y3 + y3(a − b)21a 3 − b3 + a 3 + b32a 3a 3 − b3 a 3 + b3.===+a+ba+ba+ba+b122a 3 + b 3 a 3 + b 3 + a 3 b 3 a 3 + b 3 − a 3 − b 3 − a 3 b 3 −a 3 b 3 ;==−=a−ba−ba−ba−b1334) a − b +a+b89.

1)111= 2(a 2 + b 2 );=1121 23 233x + 5x 31   131 3x + 5x 3 x 3 − x 3 + 1 3) :  4x + 4 + 1  = :+ 1+ x + 1   x + 1x + 1 5 +1 3 xx 1   1 21:  1   2x 3  + 4 ⋅ x 3 + 1  =  x3 214x 3 + 4x 3 + 1=⋅x +11x31121 23 21333 3x + 5x + x − x + 1  :  1  2x 3 + 1  =   1 x +1 3 x1x3.=x +1(2x 3 + 1) 290.

Искомая сумма вычисляется по формуле сложных процентов: S=a(++= p )t , где а — первоначальная сумма вклада, р — число процентов начисляе100мых за год, t — число лет: S=5000(1+ 2 )3 =5000(1,02)3=5306,04=5306 р. 4 коп.10091. Искомая сумма вычисляется по формуле сложных процентов:S = a(1 +7p t.) a = 2000p; p = 3; t = 212100S = 200(1 +313 2127) = 2000 ⋅ (1,03)12 = 2000 ⋅ 1,07935 = 2158,7 =185 р.

70 коп.10092. 1) (0,645: 0,3 −1107) ⋅ (4:6,25 −1:5 + 1 ⋅1,96) =  0,645 ⋅10 − 287  ⋅  4 ⋅100 − 1 + 196  =18073180625 5 7 ⋅100 387 − 287100 112 28 ; 2,15 ⋅ 180 − 287 ⋅1,12 =⋅== × (0,64 − 0,2 + 0,28) =180180 100 451802) ( 1 − 0,375) : 0,125 +  5 − 7  : (0,358 − 0,108 ) = (0,5 − 0,375 ) :2 6 12 3 410 − 7: 0,125 +: 0,25 = 0,125 : 0,125 + ⋅ = 1 + 1 = 2 .1212 193.

1) 1,3(1) = x; 100x = 131, (1); 10x = 13, (1) ;100 x − 10 x = 131, (1) − 13, (1) = 118 ;90x = 118; x = 118 = 59 = 1 14 ;9045452) 2,3( 2) = x ; 10x = 23, (2); 100 x = 232 , ( 2 ) ;100x − 10 x = 232, (2) − 23, (2) = 209 ;3) 0, ( 248 ) = x ; 1000 ⋅ x = 24,8(248) ;20929;=29090248999 ⋅ x = 248; x =;99990x = 209; x =4) 0,(34) = x; 100 ⋅ x = 34,(34) ;100 ⋅ x − x = 34,(34) − 0,(34) = 34 ;99 ⋅ x = 34; x =34.9994.

1) 48o = 1; 10 − 2 = 1 = 1 = 0,01 ;10 2 10029www.5balls.ru2 3−13 3= 1,5; (0,3) −3 =  2 10 = 12 ( −1,2) − 2 =  −  10 2)3−2327 = 33 = 3; 5= −  64−3−2=311000 10 = 111 ;=  =99 381 = 4 3 4 = 3;658 2 = 6 (2 3 ) 2 = 2 6 = 2;327 2 = 3 (33 ) 2 = 3 (32 ) 3 = 3 2 = 9 ;12−2 9= −  4−2216 ;4=  =819532 = 2 5 = 2;8618 12  425 ;3616 2 = 8 (2 4 ) 2 = 28 = 2;2113) 8 3 = (23 ) 3 = 2; 27 3 = (33 ) 3 = 32 = 9; 10000 4 = (104 ) 4 = 10;22332 5 = (25 ) 5 = 22 = 4; 32 5 = (25 )−35= 2 −3 =11= ;823222−3 323 39 27  3  3    3    3   =  3  =     =   = . 64   4    4    4  164 155 3 ⋅ 7 3 = 3 (5 ⋅ 7 )3 = 5 ⋅ 7 = 35 ; 4 324 ⋅ 4 4 = 4 324 ⋅ 4 = 6 4 = 6 ;4395.

1)5 4 2 4 125 5 4  5 =⋅ =  :858 224=5= 2,5 ;212) 56 o : 8 −2 = 1 ⋅ 8 2 = 1 ⋅ 64 = 64 ;−1154 ⋅ 5−5214471 1−= 5 4 4 ⋅ 5−2 =(0,3) 0,3 ⋅ (0,3) −1(0,3)1,396. 1) 3 −  2 431;25=172−4347−3= 731(0,3) 2=13( ) ⋅ 161 ⋅16 = 2 ;⋅ 7 −2 = 71− 2 = 7 −1 =1001= 11 .993 3 3⋅3⋅ 23− ==− ;4 244−2) (73 ⋅ 7= (0,3) 0,3−1−1,3 = (0,3) − 2 =−11118 3 ⋅   :16−1 = 2321112 22  : 9 = 15 : (3 ) = 15 : 3 = 5 ; 15 3)116 4 ⋅ 25 2 = (24 ) 4 ⋅ (52 ) 2 = 2 ⋅ 5 = 10 ;11111−−−−113⋅ 125−1 ) 3 =  3  ⋅ ((53 ) −1 ) 3 = (3−3 ) 3 ⋅ (5−3 ) 3 = 3⋅5 = 15;273 2( )3) 27 3 + 9−1 = 3323+1111= 32 + = 9 + = 9 ;9999−21114) (0,01)−2 :100− 2 =  1  ⋅ 100− 2 = (100 )2 ⋅ (102 ) 2 = 10000 ⋅10 = 100000 ;10030www.5balls.ru1;71−1−−12225)  64   8  =   8   ⋅ 5 = 9 ⋅ 5 = 45 ; 81   5   9   8 8 8 6422336)  2 10   3  =  64  ⋅ 9 =   3  27   4   27  16   4 −97.

1)2)4−2323 981 . ⋅ =1625633 3 1 3 3 3 9 3 3 ⋅ 9 3 27 3  3 3⋅ 2 =⋅===   = = 1,5 ;24242⋅482233 4 4 4 3 4 27 4 3 ⋅ 27 4  3 ⋅ 6 =⋅==  44444⋅424=3= 1,5 ;243) 4 15 5 : 4 2 = 4 125 : 4 2 = 4 125 : 2 = 4 125 ⋅ 5 = 4  5  = 5 = 2,5 ;858588⋅2522334) 3 11 1 : 3 3 1 = 3 45 : 3 10 = 3 45 : 10 = 3 45 ⋅ 3 = 3 9 ⋅ 3 = 3  3  = = 1,5 ;45) (6) (33423244 ⋅ 1036 3 26 66682227 ) = ( 6 27) = ( 3 ) = 3 = 3 ;316 )2 = ( 6 16)3 = ( 42 )3 = 46 = 4 .−3198. 1) 13,75 = 1; 2 −1 = 1 = 0,5;   =23=8, т.к. 8>1>0,5, то222) 980=1,  3 −17=−3 1  >13,75>2–1; 21113715= 2 , 32 5 = (2 ) 5 =2, т.к. 2 >2>1, то  7377−11> 32 5 >980.116616 6 699.

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