\(\frac{33.44^2+55^3.33}{45.33^2-99.33^4}\)

\(=\frac{33.121.16+121.25.33}{5.9.33^2-11.9.33^2.33^2}\)

\(=\frac{33.121\left(16+25\right)}{1089.9.\left(5-11.1089\right)}\)

\(=\frac{3993.41}{9801.\left(-11974\right)}\)

\(=-\frac{163713}{117357174}\).

\(\frac{33.44^2+55^3.33}{45.33^2-99.33^4}\)

=\(\frac{33.\left(4.11\right)^2+\left(5.11\right)^3.33}{9.5.33^2-9.11.33^4}\)

=\(\frac{33.16.11^2+125.11^3.33}{33^2.9.\left(5-11.33^2\right)}\)

= \(\frac{33.11^2.\left(16+125.11\right)}{33^2.9.\left(-11974\right)}\)

= \(\frac{132.1391}{33.9.\left(-107766\right)}\)

=  \(\frac{183612}{-32006502}\)

mik ko chắc chắn lắm

\(\frac{5}{22}\cdot\frac{33}{17}+\frac{15\cdot101}{34}-\frac{30}{34}=\frac{5\cdot11\cdot3}{17\cdot11\cdot2}+\frac{15\cdot101-15\cdot2}{34}=\frac{15}{34}+\frac{15.99}{34}\)

=100*15/34=1500/34 (bấm máy tính) = 44.1176471....

a) \(3.5^2+15.2^2-26\div2\)

= 3.25 + 15.4 - 13

= 75 + 60 - 13

= 135 - 13

= 122

b) \(5^3.2-100\div4+2^3.5\)

= 125.2 - 25 + 8.5

= 250 - 25 + 40

= 225 + 40

= 265

c)\(6^2\div9+50.2-3^3.33\)

= 36 : 9 + 100 - 9.33

= 4 + 100 - 297

= 104 - 297

= -193

d)\(3^2.5+2^3.10-81\div3\)

= 9.5 + 8.10 - 27

= 45 + 80 - 27

= 125 - 27

= 98

e) \(5^{13}\div5^{10}-25.2^2\)

= 5³ - 25.4

= 125 - 100

= 25

f) \(20\div2^2+5^9\div5^8\)

= 20 : 4 + 5

= 5 + 5

= 10

1: \(347\cdot2^2-2^2\cdot\left(216+184\right):8\)

\(=347\cdot4-4\cdot400:8\)

\(=347\cdot4-4\cdot50=4\cdot\left(347-50\right)=4\cdot297=1188\)

2: \(132-\left\lbrack116-\left(132-128\right)^2\right\rbrack\)

\(=132-\left\lbrack116-4^2\right\rbrack\)

=132-(116-16)

=132-100

=32

3: \(16:\left\lbrace400:\left\lbrack200-\left(37+46\cdot3\right)\right\rbrack\right\rbrace\)

=16:{400:[200-(37+138)]}

=16:{400:[200-175]}

=16:{400:25}

=16:16

=1

4: \(\left\lbrace184:\left\lbrack96-124:31\right\rbrack-2\right\rbrace\cdot3651\)

\(=\left\lbrace\frac{184}{96-4}-2\right\rbrace\cdot3651\)

=(184:92-2)*3651

=0

5: \(46-\left\lbrack\left(16+71\cdot4\right):15\right\rbrack-2\)

=46-[(16+284):15]-2

=46-300:15-2

=46-20-2

=46-22

=24

6: \(3^3\cdot18+72\cdot4^2-41\cdot18\)

\(=18\left(3^3-41\right)+72\cdot16\)

\(=18\cdot\left(27-41\right)+18\cdot64\)

=18(-14+64)

=18*50

=900

7: \(\left(56\cdot46-25\cdot23\right):23\)

\(=56\cdot\frac{46}{23}-25\)

=112-25

=87

8: \(\left(28\cdot54+56\cdot36\right):21:2\)

\(=18\cdot28\left(3+2\cdot2\right):42\)

\(=18\cdot\frac{28}{42}\cdot7=18\cdot\frac23\cdot7=12\cdot7=84\)

9: \(\left(76\cdot34-19\cdot64\right):\left(38\cdot9\right)\)

\(=\frac{19\cdot\left(4\cdot34-64\right)}{38\cdot9}=\frac{4\cdot34-64}{9\cdot2}=\frac{4\cdot\left(34-16\right)}{18}=4\)

10: \(\left(2+4+6+\cdots+100\right)\cdot\left(36\cdot333-108\cdot111\right)\)

\(=\left(2+4+6+\cdots+100\right)\cdot36\cdot111\left(3-3\right)\)

=0

11: \(\left(5\cdot4^{11}-3\cdot16^5\right):4^{10}\)

\(=\left(5\cdot4^{11}-3\cdot4^{10}\right):4^{10}\)

\(=5\cdot\frac{4^{11}}{4^{10}}-3\cdot\frac{4^{10}}{4^{10}}\)

=20-3

=17

12: \(\frac{7256\cdot4375-725}{3650+4375\cdot7255}=\frac{7255\cdot4375+4375-725}{7255\cdot4375+3650}\)

\(=\frac{7255\cdot4375+3650}{7255\cdot4375+3650}\)

=1

Bài làm:

a) 101² Sử dụng hằng đẳng thức thứ 1 ta có: 
= (100 + 1)² 
= 100² + 2.100.1 + 1² 
= 10000 + 200 + 1 
= 10201 
b) 199² Sử dụng hằng đẳng thức thứ 2 ta có: 
= (200 - 1)² 
= 200² - 2.200.1 + 1² 
= 40000 - 400 + 1 
= 39601 
c) 47 . 53 Sử dụng hằng đẳng thức thứ 3 ta có: 
= (50 - 3)(50 + 3) 
= 50² - 3² 
= 2500 - 9 
= 2491.

a,=10201

b,=39601

c,=2491

Nen a<b>c

1+2+3+4+5+6

= (1+6) x 3

= 7 x 3

= 21

11+22+33+44+55+66

= (11+66) x 3

= 77 x 3 

= 231

a/1 + 2 + 3 + 4 + 5 + 6

= (1 + 4 ) + (2 + 3) + 5 + 6

= 5 + 5 + 5 + 6

= 15 + 6

= 21

b/ 11+ 22 + 33 + 44 + 55 + 66

=(11+ 66) + (22 + 55) + (33 + 44)

= 77 + 77 + 77

= 77 x 3

=231

a:

Số số hạng của dãy số 1;2;3;...;102 là:

\(\frac{102-1}{1}+1=\frac{101}{1}+1=101+1=102\) (số)

1-2+3-4+5-6+...+101-102+103

=(1-2)+(3-4)+(5-6)+...+(101-102)+103

\(=\left(-1\right)+\left(-1\right)+\cdots+\left(-1\right)+103\)

\(=\left(-1\right)\cdot\frac{102}{2}+103=103-51=52\)

b: Sửa đề: 2-4+6-8+10-12+...+98-100+102

Số số hạng của dãy số 2;4;6;8;...;98;100 là:

\(\frac{100-2}{2}+1=\frac{98}{2}+1=49+1=50\) (số)

2-4+6-8+10-12+...+98-100+102

=(2-4)+(6-8)+(10-12)+...+(98-100)+102

=(-2)+(-2)+...+(-2)+102

\(=-2\cdot\frac{100}{2}+102\)

=-100+102

=2

c: Số số hạng trong dãy 16;18;20;22;...;64;66 là:

\(\frac{66-16}{2}+1=\frac{50}{2}+1=25+1=26\) (số)

16-18+20-22+...+64-66+68

=(16-18)+(20-22)+...+(64-68)+68

=(-2)+(-2)+...+(-2)+68

\(=\left(-2\right)\cdot\frac{26}{2}+68\)

=68-13

=55