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(32.5.79).(35.53):(33.52.75)2
=(3².5.79).(35.5³):(36.5⁴.710)
=(32.35:36).(5.53:54).(79.710)
=32+5-6. 51+3-4. 79+10
=31. 5 . 719
A= 136.(25+75) - (6.10)2 = 136 . 100 - 602 = 13600 - 3600 = 10000
B= (2.5)3 - {(7.2)2 - 52. [43 : 23 + 112 : 112 - 2(37 -35)]}
=103 - {142 - 52 .[(4:2)3 + (11:11)2 - 2.2]} = 1000 - { 154 - 25 .[8 + 1 -4]} = ....
= ( 2^3 . 5 . 7 ) .( 5^2.7^3)/ (2^2 . 5^2 . 7^4)
= ( 2^3 . 5 . 7 ) .(1/7.4)
= ( 8 . 5 . 7) .1/ 28
= 280. 1/28
= 10
(23.5.7)(52.7)
=(5.7)(23.5)
=35(8.5)
=35.40
=140
(2.5.72)2
=(10.49)2
=4902
=240100
1) 279 : 81 = (33)9 : 34 = 327 : 34 = 323
2) a) = 170.3 + 154 : 14 = 510 + 11 = 521
b) = 136.(25 + 75) - 72 = 13600 - 49 = 13 551
c) = (2.5)3 - [(7.2)3 - 25.(64: 8 + 121 : 121 - 2.2)] = 1000 - [2744 - 25.(8 + 1 - 4)] = 1000 - 2619 = 1619
\(\dfrac{\left(2^3.5.7\right)\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}=\dfrac{2^3.5^37^4}{2^2.5^27^4}=2.3=6\)
72x-3 -5.72 = 7 2 .2
72 .7x - 3 - 5 . 72 = 72 .2
72 . 7x - 3 = 72 .2 + 5.72
72 . 7x - 3 = 72.7
72 .7x-3 = 7 3
7x - 3 = 73 : 72
7x - 3 = 71
x - 3 = 1
x = 1+3
x = 4
Bài giải
\(B=1\cdot2^2+2\cdot3^2+3\cdot4^2+...+99\cdot100^2\)
\(B=1\cdot2\cdot\left(3-1\right)+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-1\right)+...+99\cdot100\cdot\left(101-1\right)\)
\(B=1\cdot2\cdot3-1\cdot2+2\cdot3\cdot4-2\cdot3+...+99\cdot100\cdot101-99\cdot100\)
\(B=\left(1\cdot2\cdot3+2\cdot3\cdot4+...+99\cdot100\cdot101\right)-\left(1\cdot2+2\cdot3+...+99\cdot100\right)\)
Đặt \(C=1\cdot2\cdot3+2\cdot3\cdot4+...+99\cdot100\cdot101\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot\left(5-1\right)+...+99\cdot100\cdot101\cdot\left(102-98\right)\)
\(4C=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4+...+99\cdot100\cdot101\cdot102-98\cdot99\cdot100\cdot101\)
\(4C=99\cdot100\cdot101\cdot102\)
\(4C=101989800\)
\(C=101989800\text{ : }4\)
\(C=25497450\)
Ta có: \(A=\dfrac{2^3\cdot5\cdot7\cdot5^2\cdot7^3}{\left(2\cdot5\cdot7^2\right)^2}\)
\(=\dfrac{2^3\cdot5^3\cdot7^4}{2^2\cdot5^2\cdot7^4}=\dfrac{10\cdot2^2\cdot5^2}{2^2\cdot5^2}\)
=10
\(A=\dfrac{(2^3.5.7).(5^2.7^3)}{(2.5.7^2)^2}\)
\(=\dfrac{2^3.5^3.7^4}{2^2.5^2.7^4}\)
\(=2.5\)
\(=10\)