\(\left(-\dfrac{10}{3}\right)^5.\left(-\dfrac{6}{5}\right)^4\\ =\left(-\dfrac{10}{3}\right)^5.\left(\dfrac{6}{5}\right)^4\\ =-\left(\dfrac{10}{3}\right)^5.\left(\dfrac{6}{5}\right)^4\\ =-\dfrac{10^5.6^4}{3^5.5^4}=-\dfrac{2^5.5^5.3^4.2^4}{3^5.5^4}\\ =-\dfrac{2^9.3^4.5^4.5}{3.3^4.5^4}\\ =-\dfrac{2^9.5}{3}=-\dfrac{2560}{3}\)

\(=\dfrac{-100000}{243}\times\dfrac{1296}{625}=\dfrac{\left(-100000\right).1296}{243.625}=\dfrac{\left(-160\right).625.1296}{625.243}=\dfrac{-160.1296}{243}=\dfrac{81.16.\left(-160\right)}{81.3}=\dfrac{16.\left(-160\right)}{3}=\dfrac{-2560}{3}\)

`@` `\text {Ans}`

`\downarrow`

\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2\)

`=`\(\left(\dfrac{6}{14}+\dfrac{7}{14}\right)^2\)

`=`\(\left(\dfrac{13}{14}\right)^2=\dfrac{169}{196}\)

\(\left(\dfrac{3}{7}+\dfrac{1}{2}\right)^2=\left(\dfrac{6}{14}+\dfrac{7}{14}\right)^2\\ =\left(\dfrac{13}{14}\right)^2=\dfrac{169}{196}\)

a<b

Hôm nay olm.vn sẽ hướng dẫn các em so sánh lũy thừa bằng lũy thừa trung gian. 

a = 15⁸ và b = 8¹¹

15⁸ < 16⁸ = (2⁴)⁸ = 2³²

8¹¹ = (2³)¹¹ = 2³³

Vì 2³² < 2³³ nên 15⁸ < 8¹¹

Vậy  a <  b 

180 : ( 18 x 5 )

= 180 : 90

= 2

b) 240 : ( 2 x 3 x 4 )

= 240 : 24

= 10

c) 4400 : ( 22 x 35 ) 

= 4400 : 770

= \(\dfrac{40}{7}\)

\(a\left(a+b+c\right)=10,b\left(a+b+c\right)=35,c\left(a+b+c\right)=-20\\ =>a\left(a+b+c\right)+b\left(a+b+c\right)+c\left(a+b+c\right)=10+35+\left(-20\right)\\ =>\left(a+b+c\right)^2=25\\ =>\left[{}\begin{matrix}a+b+c=5\\a+b+c=-5\end{matrix}\right.\)

TH1 : `a+b+c=5`

\(=>\left\{{}\begin{matrix}a=10:5=2\\b=35:5=7\\c=-20:5=-4\end{matrix}\right.\)

TH2 : `a+b+c=-5`

\(=>\left\{{}\begin{matrix}a=10:\left(-5\right)=-2\\b=35:\left(-5\right)=-7\\c=\left(-20\right):\left(-5\right)=4\end{matrix}\right.\)

Vậy : \(\left(a;b;c\right)=\left(2;7;-4\right);\left(-2;-7;4\right)\)

Ta có:

\(a\times\left(a+b+c\right)+b\times\left(a+b+c\right)+c\times\left(a+b+c\right)=10+35+\left(-20\right)\)

\(\left(a+b+c\right)\times\left(a+b+c\right)=25\)

\(\left(a+b+c\right)^2=5^2\)

\(a+b+c=5\)

Thay \(a+b+c=5\) ta có: \(a\times5=10\) 

                                               \(a=10\div5\) 

                                                \(a=2\) 

Thay \(a+b+c=5\) ta có: \(b\times5=35\) 

                                                \(b=35\div5\) 

                                                 \(b=7\) 

Thay \(a+b+c=5\) ta có: \(c\times5=-20\) 

                                                \(c=-20\div5\) 

                                                \(c=-4\) 

Vậy chữ số \(a,b,c\) cần tìm là \(a=2,b=7,c=-4\)

Hiệu 2 số là :

    \(2\times8+1+1=18\)

Số chẵn bé là :

     \(\left(220-18\right):2=101\)

Số chẵn lớn là :

     \(101+18=119\)

Mà đề bài yêu cầu 2 số chẵn -> 101 và 119 không thỏa mãn

Vậy không có 2 số chẵn có tổng = 220 mà giữa chúng có 9 số lẻ 

a) -3 < x < 3

=> \(x=-2;-1;0;1;2\) 

Tổng x là \(-2+\left(-1\right)+0+1+2=0\) 

b) \(-5\le x< 4\) 

=> \(x=-5;-4;-3;-2;-1;0;1;2;3\) 

Tổng x là \(-5+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3=-9\) 

c) -7 < x < 11

=> \(x=-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7;8;9;10\) 

Tổng x là  

\(-6+\left(-5\right)+\left(-4\right)+\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4+5+6+7+8+9+10=34\)

d) \(15\le x\le13\) 

Không có x nào thoả mãn đề bài

a) -2;-1;0;1;2

b)-5;-4;-3;-2;-1;0;1;2;3

c)-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7;8;9;10

d) mình chịu nhé

a) \(\left(-214\right)+\left(-120\right)+\left(-16\right)\)

\(=\left[\left(-214\right)+\left(-16\right)\right]+\left(-120\right)\)

\(=\left(-230\right)+\left(-120\right)\)

\(=-350\)

b) \(34+\left(-100\right)+\left(-34\right)+100\)

\(=\left[34+\left(-34\right)\right]+\left[\left(-100\right)+100\right]\)

\(=0+0\)

\(=0\)

c) \(\left(-2021\right)+\left(-999\right)+21+\left(-2001\right)\)

\(=\left[\left(-2021\right)+21\right]+\left[\left(-999\right)+\left(-2001\right)\right]\)

\(=\left(-2000\right)+\left(-3000\right)\)

\(=-5000\)

d) \(-41\left(59+2\right)+59\left(41-2\right)\)

\(=-41.61+59.39\)

\(=-2501+2301\)

\(=-200\)

e) \(\left(-157\right).\left(127-316\right)-127.\left(316-157\right)\)

\(=\left(-157\right).127+\left(-157\right)\left(-316\right)+\left(-127\right).316+\left(-127\right).\left(-157\right)\)

\(=-157.127+157.316-127.316+127.157\)

\(=\left[-\left(127.157\right)+127.157\right]+\left(157.316-127.316\right)\)

\(=0+316.\left(157-127\right)\)

\(=316.30\)

\(=9480\)

f) \(-1500-\left\{5^3.2^3-11.\left[7^2-5.2^3+8.\left(11^2-121\right)\right]\right\}.\left(-2\right)\)

\(=-1500-125.8-11.\left[49.-5.2^3.\left(121-121\right)\right]\)

\(=-1500-\left[1000-11.\left(49-0\right)\right]\)

\(=-1500-\left(1000-539\right)\)

\(=-2500+539\)

\(=-1961\)

Nếu là tìm x vậy vế phải đâu bạn ?

\(\dfrac{2}{5}+\dfrac{3}{5}:\left(\dfrac{3}{5}+-\dfrac{2}{3}\right)-\dfrac{5}{2}\)

\(=\dfrac{2}{5}+\dfrac{3}{5}:\left(-\dfrac{1}{15}\right)-\dfrac{5}{2}\)

\(=\dfrac{2}{5}+\left(-9\right)-\dfrac{5}{2}\)

\(=-\dfrac{21}{10}+-9\)

\(=-\dfrac{111}{10}\)

\(\dfrac{2}{5}+\dfrac{3}{5}\):(\(\dfrac{3}{5}\) - \(\dfrac{2}{3}\)) - \(\dfrac{5}{2}\)

= \(\dfrac{2}{5}\) + \(\dfrac{3}{5}\):(-\(\dfrac{1}{15}\)) - \(\dfrac{5}{2}\)

= \(\dfrac{2}{5}\) - 9 - \(\dfrac{5}{2}\)

= \(\dfrac{4}{10}\) - \(\dfrac{90}{10}\) - \(\dfrac{25}{10}\) 

= \(-\dfrac{111}{10}\)