a) (-8)+10+(-12)+14+...+(-32)+34+(-36)+38 

=(-8+10)+(-12+14)+...+(-32+34)+(-36+38)

=2+2+...+2+2 ( Có 16 số 2)

=2.16

=32

Trả lời:

\(a)\)\(\left(-8\right)+10+\left(-12\right)+14+...+\left(-32\right)+34+\left(-36\right)+38\)(Có 16 số)

\(=\left[\left(-8\right)+10\right]+\left[\left(-12\right)+14\right]+...+\left[\left(-36\right)+38\right]\)(Có 8 nhóm)

\(=\left(-2\right)+\left(-2\right)+...+\left(-2\right)\)

\(=\left(-2\right).8\)

\(=-16\)

\(b,\)\(1+3+5+...+49-2-4-6-...-50\)

\(=\left(1-2\right)+\left(3-4\right)+...+\left(49-50\right)\)(Có 25 nhóm)

\(=\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

\(=\left(-1\right).25\)

\(=-25\)

Hok tốt!

Good girl

a) (1/4)³ x (1/8)²

= [(1/2)²]³ x [(1/2)³]²

= (1/2)⁶ x (1/2)⁶

= (1/2)¹²

b) 4² x 32: 2³

= (2²)² x 2⁵: 2³

= 2⁴ x 2⁵: 2³

= 2⁴ x 2²

= 2⁶

c) 25 x 5³ x 1/625 x 5³

= 5²x 5³ x (1/5)⁴ x 5³ 

= (1/5)⁴ x 5⁸

= 1/5⁴ x 5⁸ (giải thích nếu ko hiểu: (1/5)⁴= 1⁴/5⁴= 1/5⁴)

= 5⁸/5⁴

= 5⁴ 

d) 5⁶ x 1/20 x 2² x 3² : 125

= 5⁶/20 x (2x3)² : 5³

= 5⁶/ (5x4) x 6²: 5³

= 5⁵/4 x 6²/5³ (6²/5³ là dạng phân số, bản chất vẫn là lấy 6² chia 5³)

= 5⁵ x 6²/ 4x 5³ (nhân phân số: tử nhân tử, mẫu nhân mẫu)
= 5²x 6²/ 2² (chia 5⁵ cho 5³ ra 5²)

= 30²/ 2²

= 15²

*Kiến thức áp dụng:
a^mx aⁿ = a^m+n

a^m: aⁿ= a^m-n

(a^m)ⁿ = a^{m x n}

a^m x b^m = (a x b)^m

khôngn đăng lại

a, \(\frac{3}{10}+\frac{5}{8}=\frac{24}{80}+\frac{50}{80}=\frac{74}{80}=\frac{37}{40}\)

b, \(\frac{1}{8}+\frac{5}{6}=\frac{3}{24}+\frac{20}{24}=\frac{23}{24}\)

c, \(\frac{1}{3}+\frac{1}{6}+\frac{1}{8}=\frac{8}{24}+\frac{4}{24}+\frac{3}{24}=\frac{15}{24}=\frac{5}{8}\)

#Fox

a) 67+135+33

= ( 67+33)+135

= 100 + 135

= 235

b) 146+121+54+379

= ( 146+54)+( 121+379)

= 200 + 500

= 700

c) 198+232-98-32

= ( 232-32)+(198-98)

= 200 + 100

= 300

d)1+2+3+4+.........+50

= ( 50+1) x 50:2 =1275

e)2+4+6+8+..........+100

= ( 100+2) x 50 : 2 =2550

f) 23 x 56 +56

= 1288 + 56

= 1344

g)32 x 19+32

= 608 + 32

= 640

\(a.67+135+33\)

\(=\left(67+33\right)+135\)

\(=100+135=235\)  

\(b.141+121+54+379\)

\(=\left(146+54\right)+\left(121+379\right)\)

\(=200+500=700\)

\(c.198+232-98-32\)

\(=\left(232-32\right)+\left(198-98\right)\)

\(=200+100=300\)

\(f.23.56+56=1288+56=1344\)

\(g.32.19+32=608+32=640\)

a) \(\dfrac{13}{20}+\dfrac{3}{5}+x=\dfrac{5}{6}\)

\(\Rightarrow\dfrac{5}{4}+x=\dfrac{5}{6}\)

\(\Rightarrow x=\dfrac{5}{6}-\dfrac{5}{4}\)

\(\Rightarrow x=\dfrac{-5}{12}\)

b) \(x+\dfrac{1}{3}=\dfrac{2}{5}-\dfrac{-1}{3}\)

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{11}{15}\)

\(\Rightarrow x=\dfrac{11}{15}-\dfrac{1}{3}\)

\(\Rightarrow x=\dfrac{2}{5}\)

c)\(\dfrac{-5}{8}-x=\dfrac{-3}{20}-\dfrac{-1}{6}\)

\(\dfrac{-5}{8}-x=\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-5}{8}-\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-77}{120}\)

d) \(\dfrac{3}{5}-x=\dfrac{1}{4}+\dfrac{7}{10}\)

\(\Rightarrow\dfrac{3}{5}-x=\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{3}{5}-\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{-7}{20}\)

e) \(\dfrac{-3}{7}-x=\dfrac{4}{5}+\dfrac{-2}{3}\)

\(\Rightarrow\dfrac{-3}{7}-x=\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-3}{7}-\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-59}{105}\)

g) \(\dfrac{-5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)

\(\Rightarrow\dfrac{-5}{6}-x=\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-13}{12}\)

7 = 3 + 4 = √9 + √16

Do 10 > 9 nên √10 > √9

17 > 16 nên √17 > √16

⇒ √10 + √17 > √9 + √16

Vậy √10 + √17 > 7

--------

(1/8)²³ = 1/(2³)²³ = 1/2⁶⁹

(1/32)¹⁶ = 1/(2⁵)¹⁶ = 1/2⁸⁰

Do 69 < 80 nên 2⁶⁹ < 2⁸⁰

⇒ 1/2⁶⁹ > 1/2⁸⁰

Vậy (1/8)²³ > (1/³²)¹⁶

--------

5 = √25

Do 27 > 25 nên √27 > √25

Vậy √27 > 5

\(\dfrac{3}{10}+\dfrac{5}{8}\)
\(=\dfrac{12}{40}+\dfrac{25}{40}=\dfrac{37}{40}\)

\(\dfrac{3}{10}+\dfrac{5}{8}=\dfrac{24}{80}+\dfrac{50}{80}=\dfrac{24+50}{80}=\dfrac{74}{80}=\dfrac{37}{40}\)

\(\dfrac{3}{10}+\dfrac{5}{8}=\dfrac{24}{80}+\dfrac{50}{80}=\dfrac{74}{80}=\dfrac{37}{40}\)