a: \(\dfrac{1}{7}\cdot\dfrac{3}{8}+\dfrac{1}{7}\cdot\dfrac{5}{8}+\dfrac{\left(-1\right)^{2023}}{7}\)

\(=\dfrac{1}{7}\left(\dfrac{3}{8}+\dfrac{5}{8}\right)-\dfrac{1}{7}\)

\(=\dfrac{1}{7}-\dfrac{1}{7}=0\)

b: \(-3-\dfrac{16}{23}-\sqrt{\dfrac{4}{49}}-\dfrac{7}{23}+\dfrac{\left(-3\right)^2}{7}\)

\(=-3-\left(\dfrac{16}{23}+\dfrac{7}{23}\right)-\dfrac{2}{7}+\dfrac{9}{7}\)

\(=-3-\dfrac{23}{23}+\dfrac{7}{7}\)

=-3-1+1

=-3

c: \(\dfrac{4^2\cdot0,2^3}{2^6}\)

\(=\dfrac{2^4\cdot0,008}{2^6}=\dfrac{0.008}{4}=0.002\)

Haha

a, \(\dfrac{7}{22}\) - \(\dfrac{15}{23}\) + \(\dfrac{2022}{2023}\) - \(\dfrac{8}{23}\) + \(\dfrac{15}{22}\)

= ( \(\dfrac{7}{22}\) + \(\dfrac{15}{22}\)) - ( \(\dfrac{15}{23}+\dfrac{18}{23}\)) + \(\dfrac{2022}{2023}\)

= \(\dfrac{22}{22}\) - \(\dfrac{23}{23}\) + \(\dfrac{2022}{2023}\)

= 1 - 1 + \(\dfrac{2022}{2023}\)

= \(\dfrac{2022}{2023}\) 

b, - \(\dfrac{2}{11}\) + 5\(\dfrac{5}{6}\) ( 14\(\dfrac{1}{5}\) - 11\(\dfrac{1}{5}\)): 5\(\dfrac{1}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) ( \(\dfrac{71}{5}\) - \(\dfrac{56}{5}\)) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{6}\) . \(\dfrac{15}{5}\) : \(\dfrac{11}{2}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{2}\) \(\times\) \(\dfrac{2}{11}\)

= - \(\dfrac{2}{11}\) + \(\dfrac{35}{11}\)

= \(\dfrac{33}{11}\)

= 3 

c, 2000 + { 20 - [ 4.2022⁰ - (3² + 5):2] }

= 2000 + { 20 - [ 4.1 - (9+5):2]}

= 2000 + { 20 - [ 4 - 14 : 2 ]}

= 2000 + { 20 - [ 4 -7]}

= 2000 + { 20 - (-3)}

= 2000 + 23

= 2023

5 ( năm )

a, <=> (x-5/100) -1 +(x-4/101) -1 +(x-3/102) -1= (x-100/5) -1+(x-101/4) -1 +(x-102/3) -1
<=> (x-105)(1/100 +1/101 +1/102)= (x-105)(1/5+1/4+1/3)
<=> (x-105)(1/100+1/101+1/102-1/5-1/4-1/3)=0
vì 1/100+1/101+1/102-1/5-1/4-1/3 khác 0 <=> x-105=0
<=> x=105

b, 29-x/21 +1+27-x/23 +1+25-x/25 +1+23-x/27 +1+21-x/29 +1=0
<=> 50-x/21 +50-x/23 +50-x/25 +50-x/27 +50-x/29=0
<=> (50-x)(1/21 +1/23 +1/25 +1/27 +1/29)=0
vì 1/21+1/23+1/25+1/27+1/29 lớn hơn 0
nên 50-x=0
<=> x=50

2023 - 3 * x - 7 * x = 23 + 990 * x

2023 - 23 - x * ( 3 + 7 ) = 990 * x

2000 - x * 10 = 990 * x

2000 = 990 * x + x * 10

2000 = x * ( 990 + 10 )

2000 = x * 1000

x = 2

Lời giải:

$A=(21-23)+(25-27)+....+(2021-2023)$

$=(-2)+(-2)+...+(-2)$

Số lần xuất hiện của $-2$ là: $[(2023-21):2+1]:2=501$

$A=501(-2)=-1002$

$B=(1-2-3+4)+(5-6-7+8)+....+(1997-1998-1999+2000)$

$=0+0+0+...+0=0$

\(27.77+24.27-27\)

\(=27.\left(77+24-1\right)\)

\(=27.100\)

\(=2700\)

\(174\div\left\{2\left[36+\left(4^2-23\right)\right]\right\}\)

\(=174\div\left\{2\left[36+\left(16-23\right)\right]\right\}\)

\(=174\div\left\{2\left[36+\left(-7\right)\right]\right\}\)

\(=174\div\left\{2.29\right\}\)

\(=174\div58\)

\(=3\)

\(3^2.4-\left[30-\left(5-2\right)^2\right]\)

\(=9.4-\left[30-3^2\right]\)

\(=36-\left[30-9\right]\)

\(=36-21\)

\(=15\)