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а) 8 = 23; б) 81 = 92; в) 125 = 53; г) 64 = 82 = 43; д) 0,001 = 0,13;−223 27 ⎛ 3 ⎞11 36 ⎛ 6 ⎞= ⎜ ⎟ ; ж) 1 ==⎜ ⎟ .е) 3 =8 8 ⎝2⎠25 25 ⎝ 5 ⎠№394. а) 712 > 0; б) (–25)3 < 0; в) (–5,9)3 < (–5,9)2; г) (–2,3)12 > (–8,6)19.№395.а) 7 ⋅ 52 = 7 ⋅ 25 = 175;б) (7 ⋅ 5)2 = 352 = 1225;в) (–0,4)3 = –0,064;г) –0,043 = –0,064;5д) –3 ⋅ 2 = –3 ⋅ 32 = –96; е) –62 ⋅ (–12) = –36 ⋅ (–12) = 432.№396.а) 342 – 175 = 1156 – 175 = 981;б) 605 + 782 = 605 + 6084 = 6689;2г) 182 : 27 = 324 : 27 = 12;в) 42 ⋅ 9 = 1764 ⋅ 9 = 15876;22д) 75 + 25 = 5625 + 625 = 6250; е) 592 – 362 = 3481 – 1296 = 2185.22225 251225⎛5⎞⎛ 5 ⎞ ⎛ 15 ⎞== 6 ; б) ⎜ 9 ⋅ ⎟ = ⎜ ⎟ == 56 ,25 ;а) 9 ⋅ ⎜ ⎟ = 9 ⋅36 444⎝6⎠⎝ 6⎠ ⎝ 2 ⎠в) (–10)6 = 1000000;г) –106 = –1000000;е) –5 ⋅ 25 = –5 ⋅ 32 = –160;д) 4 ⋅ 53 = 4 ⋅ 125 = 500;4ж) –2 ⋅ 15 = –16 ⋅ 15 = –240; з) 2700 ⋅ (–0,1)3 = 2700 ⋅ (–0,001) = –2,7.№398.а) 72 + 32 = 49 + 27 = 76;б) 63 + 82 = 36 + 64 = 100;22г) 102 – 32 = 100 – 9 = 91;в) (6 + 8) = 14 = 196;д) (10–3)2=72 = 49; е) 24 – 32 = 16 – 9 = 7; ж) 11 – 34 = 11 – 81 = –70;з) (6 – 8)5 = (–2)5 = –32;и) 43 – 22 = 64 – 4 = 60.№399.а) –13 + (–2)3 = –1 – 8 = –9;б) –62 – (–1)4 = –36 – 1 = –37;33в) –8 + (–3) = –512 – 27 = –539; г) 10 – 5 ⋅ 24 = 10 – 80 = –70;д) 2 ⋅ 34 – 3 ⋅ 24 = 162 – 48 = 114; е) 2 ⋅ 53 + 5 ⋅ 23 = 250 + 40 = 290;№397.214 25⎛2⎞= 81 − 1 = 80 ;ж) 34 – ⎜ ⎟ ⋅ 6 = 81 − ⋅425 4⎝5⎠з) 0,2 ⋅ 33 – 0,4 ⋅ 24 = 5,4 – 6,4 = –1; и) 8 ⋅ 0,53 + 25 ⋅ 0,22 = 1 + 1 = 2.№400.а) при x = –2, 8х3 = 8 ⋅ (–2)3 = –64, при x = –1, 8х3 = 8 ⋅ (–1)3 = –8,при x = 0, 8х3 = 8 ⋅ 03 = 0, при x = 3, 8х3 = 8 ⋅ 33 = 216;б) при a = –25, 70 – a2 = 70 – (–25)2 = –555,при a = 1, 70 – a2 = 70 – 12 = 69, при a = 10, 70 – a2 = 70 – 102 = –30.50№401.

а) при y = –2, 0,01y4 = 0,01 ⋅ (–2)4 = 0,01 ⋅ 16 = 0,16,при y = 3, 0,01y4 = 0,01 ⋅ 34 = 0,01 ⋅ 81 = 0,81,при y = 10, 0,01y4 = 0,01 ⋅ 104 = 0,01 ⋅ 10000 = 100;б) при c = –11, 2с3 + 3 = 2 ⋅ (–11)2 + 3 = 2 ⋅ 121 + 3= 245,при c = 0, 2с3 + 3 = 2 ⋅ 02 + 3 = 3,при c = 15, 2с3 + 3 = 2 ⋅ 152 + 3 = 2 ⋅ 225 + 3 = 453.№402.а) при x = 9, х2 = 81; –х2 = –81; (–х)2 = (–9)2 = 81,при x = –6, х2 = 36; –х2 = –36; (–х)2 = 62 = 36;б) при x = 4, х3 = 64; –х3 = –64; (–х)3 = (–4)3 = –64;при x = –3, х3 = –27; –х3 = 27; (–х)3 = 33 = 27.№403.

при x = –1, x5 + x4 + x3 + x2 + x = –1 + 1 – 1 + 1 – 1 = –1,при x = 0, x5 + x4 + x3 + x2 + x = 0 + 0 + 0 + 0 + 0 = 0,при x = 10, x5 + x4 + x3 + x2 + x = 100000 + 10000 + 1000 + 100 + 10 = 111110.№404.при x = 5, 2x4 – 5x3 + x2 + 3x + x = 2 ⋅ 54 – 5 ⋅ 53 + 52 + 3 ⋅ 5 = 665,при x = –5, 2x4–5x3+x2+3x+x=2⋅(–5)4+5 ⋅ (–5)3 + (–5)2 – 3 ⋅ (–5) = 1885.№405.а) a3a = аааа = a4; б) a4a2 = аааааа = a6;32в) a3a6 = ааааааааа = a9; г) a20a12 = aa...a{ ⋅ aa...a{=a .2012№406.4x2 ≥ 0 и (x – 8)2 ≥ 0 для любого x, т.к. квадрат любого числа есть число неотрицательное.№407.a2 + 1 > 0 и 3 + (5 – a)2 > 0 при любых a, так как a2 > 0 и (5 – a)2 ≥ 0, сумманеотрицательного и положительного выражений положительна.№408.а) (x + 1)2; б) a2 + b2; в) m2 – n2; г) (m – n)2; д) 2x2y2; е) 2а3b2.№409.а) Квадрат суммы чисел x и y; б) Сумма квадратов чисел x и y;в) Квадрат разности чисел x и y; г) Разность квадратов чисел x и y;д) Куб разности чисел x и y;е) Сумма кубов чисел x и y;ж) Удвоенный квадрат разности чисел a и b;з) Утроенная сумма квадратов чисел a и b;№410.

y = 1,2x –30; пересечение с Ox: 1,2x – 30 = 0; 1,2x = 30;x = 25; A(25; 0); с Oy: y = 1,2 ⋅ 0 –30; y = –30; B(0; –30).№411.а) –4x + 1,3 = x – 2,7, –5x = –4, x = 0,8, y = –1,9, A(0,9; –1,9);б) –x + 8,1 = –3x + 7,9, 2x = –0,2, x = –0,1, y = 8,2, B(–0,1; 8,2).№412.111а) y = – x + 3 и y = – x –3 параллельны, т.к. k1 = k2 = – ;22222б) y = x + 4 и y = – x + 4, пересекаются в точке (0; 4).335117. Умножение и деление степеней№413.а) x5x8 = x13;б) a6a3 = a9;в) y4y9 = y13;г) b8b15 = b23;9 = 1012136410е)yy = y ;ж) 2 ⋅ 2 = 2 ; з) 75 ⋅ 7 = 76.д) x x x ;№414.а) m3m8 = m11; б) x4x4 = x8;в) c7c12 = c19;г) p3p11 = p14;34239817е) b b = b ;ж) 5 ⋅ 5 = 5 ; з) 33 ⋅ 33 = 36.д) aa = a ;№415.а) a15 = a6a9; б) a15 = a9a6; в) a15 = a2a13;г) a15 = a14a.№416.а) x10 = x5x5;б) y15 = y10y5; в) 212 = 25 ⋅ 27;г) 517 = 510 ⋅ 57.№417.x6 = x3x3 = x4x2 = x5x = x2x4 = xx5.№418.а) x2x5x4 = x11; б) y3y2y = y6; в) mm3m2m5 = m11; г) p4p3pp = p9;е) 34 ⋅ 32 ⋅ 33 ⋅ 3 = 310.д) 102 ⋅ 103 ⋅ 105 = 1010;№419.а) m3m2m8 = m13;б) a4a3a2 = a9;в) xx4x4x = x10;53 6158413д) 7 ⋅ 7 ⋅ 7 = 7 ; е) 5 ⋅ 52 ⋅ 53 ⋅ 55 = 511.г) n nn n = n ;№420.а) 58 ⋅ 25 = 58 ⋅ 52 = 510;б) 312 ⋅ 27 = 312 ⋅ 33 = 315;г) 29 ⋅ 32 = 2925 = 29 ⋅ 25 = 214;в) 615 ⋅ 36 = 615 ⋅ 62 = 617;д) 0,45 ⋅ 0,16 = 0,45 ⋅ 0,42 = 0,47; е) 0,001 ⋅ 0,14 = 0,13 ⋅ 0,14 = 0,17.№421.а) 24 ⋅ 2 = 25 = 32;б) 26 ⋅ 4 = 28 = 256;710в) 8 ⋅ 2 = 2 = 1024; г) 16 ⋅ 32 = 29 = 512.№422.а) 32 ⋅ 35 = 37 = 2187; б) 81 ⋅ 36 = 34 ⋅ 36 = 310 = 59049;в) 9 ⋅ 2187 = 32 ⋅ 37 = 39 = 19683; г) 27 ⋅ 243 = 33 ⋅ 35 = 38 = 6561.№423.а) (c4)2 = c4 ⋅ c4 = c8; б) (c2)4 = c2 ⋅ c2 ⋅ c2 ⋅ c2 = c8.№424.а) x5 : x3 = x2; б) y10 : y7 = y3;в) a21 : a = a20;г) b19 : b18 = b;з) 0,79 : 0,74 = 0,75.д) c12 : c3 = c9; е) p20 : p10 = p10; ж) 38 : 35 = 33;№425.а) p10 : p6 = p4; б) a8 : a4 = a4;в) x15 : x4 = x11; г) y9 : y = y8;д) 1016 : 1012 = 104; е) 2,316 : 2,37 = 2,39.№426.а) 55 : 54 = 52 = 25;б) 1015 : 1012 = 103 = 1000;862в) 0,510 : 0,57 = 0,53 = 0,125;7⎛ 1 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ 16=1 ;г) ⎜1 ⎟ : ⎜1 ⎟ = ⎜ 1 ⎟ =99⎝ 3⎠ ⎝ 3⎠ ⎝ 3⎠д) 2,7313 : 2,7312 = 2,73;8⎛ 2⎞ ⎛ 2⎞ ⎛ 2⎞е) ⎜ − ⎟ : ⎜ − ⎟ = ⎜ − ⎟ = −.33327⎝⎠ ⎝⎠ ⎝⎠75243№427.а)8684= 82 = 64 ;б)0,870,84= 0,83 = 0,512 ;4в)( − 0 ,3)5( − 0 ,3)5⎛ 1⎞2⎜1 ⎟912⎛ 1⎞г) ⎝ ⎠2 = ⎜1 ⎟ = = 2 ;244⎝⎠⎛ 1⎞⎜1 ⎟⎝ 2⎠= ( − 0 ,3)2 = 0 ,09 ;6⎛ 1⎞33⎜ −2 ⎟343193⎠⎛ 1⎞⎛7⎞д) ⎝= ⎜ −2 ⎟ = − ⎜ ⎟ = −= −12 .3332727⎝⎠⎝⎠⎛ 1⎞⎜ −2 ⎟⎝ 3⎠№428.№429.№430.79 ⋅ 75315б) 5 6 = 34 = 81 ;= 7 2 = 49 ;1273 ⋅3516 ⋅ 540 ,612в)г)= 52 = 25 ;= 0,63 = 0,216 .1850,64 ⋅ 0 ,65а) xnx3 = xn+3;б)a2am = a2+m; в) xxn = x1+n; г) yn : y4 = yn–4;9m9–mд) c : c = c ; е) kn : k = kn–1.а) 3x0 = 3 ⋅ 1 = 3; б) –2,5y0 = –2,5 ⋅ 1 = –2,5;в) 10a2b0 = 10a2 = 10 ⋅ (–3)2 = 10 ⋅ 9 = 90;а)3№431.№432.27⎛ 1⎞= −1 .г) 27a0c3 = 27c3 = 27 ⋅ ⎜ − ⎟ = −27⎝ 3⎠а) b4b0 = b4; б) c5 : c0 = c5; в) a4a0 = a4;а) 9 = 33; б) –27 = (–3)3;в) 6,25 = 2,53;№433.327 ⎛ 3 ⎞= ⎜− ⎟ ;д) −3 = −88 ⎝ 2⎠y = x – 3, при x = 4, y = 1,3г) x3 : x0 = x3.г) 0,064 = 0,43;24 49 ⎛ 7 ⎞=⎜ ⎟ .е) 5 =9 9 ⎝3⎠при x = 6, y = 3.y531–3–1–10135x–3–553№434.11ч, автомобиль прошел s = 70 ⋅ 3 = 245 км.22К моменту t = 5 ч, пройдено s = 70 ⋅ 5 = 350 км.Т.е.

за время с 3,5 ч по 5 ч автомобиль прошел 350 – 245 = 105 км.№435.а) 6a2 ≥ 0; б) –a2 ≤ 0; в) a2 + 4 > 0; г) (a + 4)2 ≥ 0; д) –a2 – 5 < 0.№436.y = x3 – 3x2A(7; 196)73 – 3 ⋅ 72 = 343 – 147 = 196 — принадлежит;B(–5; –200)(–5)3 – 3 ⋅ 52 = –125 – 75 = 200 — принадлежит.№437.К моменту t = 340 см3 — 108 г. 75 см3 — x кг.75 ⋅ 108= 202,5 г — масса куска с V=75см2.4018. Возведение в степень произведения и степени№438. а) (xy)4 = x4y4; б) (abc)5 = a5b5c5; в) (2x)3 = 8x3; г) (3a)2 = 9a2;д)(–5x)3 = –125x3; е) (–10ab)2 = 100a2b2;ж) (–0,2xy)4 = 0,0016x4y4; з) (–0,5bd)3 = –0,125b3d3.№439. а) (mn)5 = m5n5; б) (xyz)2 = x2y2z2; в) (–3y)4 = 81y4;г) (–2ax)3 = –8a3x3; д) (10xy)2 = 100x2y2;е) (–2abx)4 = 16a4b4x4; ж) (–am)3 = –a3m3; з) (–xn)4 = x4n4.№440.

а) (2 ⋅ 10)3 = 8000; б) (2 ⋅ 5)4 = 10000;в) (3 ⋅ 100)4 = 8100000000; г) (5 ⋅ 7 ⋅ 20)2 = 490000.№441.а) (–a)2 = ((–1) ⋅ a)2 = (–1)2a2 = a2; б) (–a)3 = (–a) ⋅ (–a) ⋅ (–a) = –a ⋅ a ⋅ a = –a3.№442. S = a2, при a = 2b, S = (2b)2 = 4b2, S увеличится в 4 раза;при a = 3b, S = (3b)2 = 9b2, S увеличится в 9 раз;при a = 10b, S = (10b)2 = 100b2, S увеличится в 100 раз;при a = nb, S = (nb)2 = n2b2, S увеличится в n2 раз.№443.

V = a3, при a = 2b, V = (2b)3 = 8b3, V увеличится в 8 раз;при a = 3b, V = (3b)3 = 27b3, V увеличится в 27 раз;при a = 10b, V = (10b)3 = 1000b3, V увеличится в 1000 раз;при a = nb, V = (nb)3 = n3b3, V увеличится в n3 раз.№444. а) b3x3 = (bx)3;б) a7b7 = (ab)7; в) x2y2z2 (xyz)3;г) (–a)3b3 = (–ab)3; д) 32a5 = (2a)5; е)0,027m3 = (0,3m)3.№445.

а) 24 ⋅ 54 = (10)4 = 10000;б) 43 ⋅ 253 = 1003 = 1000000;⎛2⎞⎝7⎠в) 0,2515 ⋅ 415 = 115 = 1;107г) ⎜ ⎟ ⋅ 1,57 = 17 = 1;95 5⎛ 5⎞⎛5 7⎞ 5д) ⎜ ⎟ ⋅ 1, 49 = ⎜ ⋅ ⎟ ⋅ = 19 ⋅ = ;7 7⎝ 10 ⎠⎝7 5⎠ 7е) 0,26 ⋅ 507 = (0,2 ⋅ 50)6 ⋅ 50 = 106 ⋅ 50 = 50000000.54№446. а) (x3)2 = x6; б) (x2)3 = x6; в) (a5)4 = a20; г) (a6)3 = a18; д) (y2)5 = y10;е) (y7)2 = y14; ж) (b3)3 = b9; з) (b5)2 = b10.№447.

а) (x6)4 = x24; б) x6 ⋅ x4 = x10; в) x2 ⋅ x2 = x4; г) (x2)2 = x4;д) x2 ⋅ x3 ⋅ x4 = x9; е) ((x2)3)4 = (x6)4 = x24.№448. а) (a5)2 = a10; б) a5 ⋅ a2 = a7; в) (a4)3 = a12; г) a3 ⋅ a4 = a7;д) a5 ⋅ a5 = a10; е) (a5)5 = a25.№449. а) an ⋅ a3 = an+3; б) a ⋅ am = am+1; в) a2 ⋅ am = a2+m;г) (a2)m = a2m; д) (an)3 = a3n; е) (a3)n = a3n.№450. а) 254 = (52)4 = 55; б) 1253 = (53)3 = 56; в) 6252 = (54)2 = 58.№451. а) 220 = (22)10; б) 220 = (24)5; в) 220 = (25)4; г) 220 = (210)2.№452. а) 260 = (22)30 = 430; б) 260 = (23)20 = 820;в) 260 = (24)15 = 1615; г) 260 = (25)12 = 3212.№453.

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