Phát biểu một cách hình thức như sau: các số nguyên là miền nguyên sắp xếp theo một thứ tự duy nhất mà các phần tử dương của nó được sắp xếp theo một thứ tự tốt (well-ordered), và các thứ tự đó được bảo toàn dưới phép cộng. Cũng như số tự nhiên, các số nguyên hợp thành một tập hợp vô hạn đếm được.

Số nguyên tập hợp bao gồm số 0,số nguyên dương và số nguyên âm

A= (-4+2)-(16+11)

A= -4+2-16-11

A= -2-16-11

A= -18-11

A= -29

A=(-4+2)-(16+11)

A=-4+2-16-11

A=-29

#H

\(S=\frac{5}{1\times2}+\frac{5}{2\times7}+\frac{5}{7\times5}+\frac{5}{5\times13}+...+\frac{5}{67\times35}\)

\(=\frac{10}{1\times4}+\frac{10}{4\times7}+\frac{10}{7\times10}+...+\frac{10}{67\times70}\)

\(=\frac{10}{3}\times\left(\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{67\times70}\right)\)

\(=\frac{10}{3}\times\left(\frac{4-1}{1\times4}+\frac{7-4}{4\times7}+\frac{10-7}{7\times10}+...+\frac{70-67}{67\times70}\right)\)

\(=\frac{10}{3}\times\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{67}-\frac{1}{70}\right)\)

\(=\frac{10}{3}\times\left(1-\frac{1}{70}\right)\)

\(=\frac{23}{7}\)

Trả lời:

\(\frac{5}{1.2}+\frac{5}{2.7}+\frac{5}{7.5}+\frac{5}{5.13}+...+\frac{5}{67.35}\)

\(=\frac{5.2}{1.2.2}+\frac{5.2}{2.7.2}+\frac{5.2}{7.5.2}+\frac{5.2}{5.13.2}+...+\frac{5.2}{67.35.2}\)

\(=\frac{10}{4}+\frac{10}{28}+\frac{10}{70}+\frac{10}{130}+...+\frac{10}{4690}\)

\(=\frac{10}{1.4}+\frac{10}{4.7}+\frac{10}{7.10}+\frac{10}{10.13}+...+\frac{10}{67.70}\)

\(=\frac{10.3}{1.4.3}+\frac{10.3}{4.7.3}+\frac{10.3}{7.10.3}+\frac{10.3}{10.13.3}+...+\frac{10.3}{67.70.3}\)

\(=\frac{10}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{67.70}\right)\)

\(=\frac{10}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{67}-\frac{1}{70}\right)\)

\(=\frac{10}{3}.\left(1-\frac{1}{70}\right)=\frac{10}{3}.\frac{69}{70}=\frac{23}{7}\)

=128,879

a) ƯC(220;240;300)

220=2².5.11

240=2⁴.3.5

300=2².3.5²

=> ƯCLN(220;240;300)=2².5=20

=> ƯC(220;240;330)=Ư(20)={1;2;4;5;20}

b) BC(220;240;300)

Phân tích 3 số như ý a

BCNN(220;240;300)=2⁴.3.5².11=13200

=> Bc(220;240;300)=B(13200)={0;13200;26400;...}

#H

Trả lời:

a, \(\frac{27}{36}=\frac{3.3.3}{3.3.4}=\frac{3}{4}\)

b, \(\frac{24}{128}=\frac{3.8}{16.8}=\frac{3}{16}\)

c, \(\frac{64}{216}=\frac{8.8}{8.27}=\frac{8}{27}\)

d, \(\frac{\left(-5\right)^7}{625}=\frac{-5^7}{5^4}=-5^3\)

e, \(\frac{81}{\left(-9\right)^5}=\frac{9^2}{-9^5}=\frac{1}{-9^3}=-\frac{1}{9^3}\)

f, \(\frac{900}{-30}=\frac{30.30}{-30}=-\frac{30.30}{30}=-30\)

a. \(\frac{27}{36}=\frac{3}{4}=0,75\)

b. \(\frac{24}{128}=\frac{3}{16}=0,1875\)

c. \(\frac{64}{126}=\frac{32}{63}\)

d. \(\frac{\left(-5\right)^7}{625}=\frac{-78125}{625}=-625\)

e. \(\frac{81}{\left(-9\right)^5}=\frac{81}{-59049}=\frac{-81}{59049}=\frac{-1}{729}\)

f . \(\frac{900}{\left(-30\right)}=\frac{-900}{30}=-30\)

trl

ko brt làm

ht

a) ( hình như sai nên mk chỉnh lại )

3⁵ x 27

= 3⁵ x 3³

= 3⁸

b) 7¹⁰ x 49

= 7¹⁰ x 7²

= 7¹²

c) - 2⁵ x 16

= -2⁵ x 2⁴

= -2¹

d) ( -5 ) x 625

= ( -5 ) x 5⁴

= 5³

g) ( -10 )⁵ x 100

= ( -10 )⁵ x 10²

= ( -10 )³

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+....+\frac{1}{197.200}\)

\(=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+....+\frac{1}{197}-\frac{1}{200}\)

\(=\frac{1}{5}-\frac{1}{200}\)

\(=\frac{40}{200}-\frac{1}{200}\)

\(=\frac{39}{200}\)

#H

Trả lời:

\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{197.200}\)

\(=\frac{1.3}{5.8.3}+\frac{1.3}{8.11.3}+\frac{1.3}{11.14.3}+...+\frac{1.3}{197.200.3}\)

\(=\frac{1}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{197.200}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{200}\right)=\frac{1}{3}.\frac{39}{200}=\frac{13}{200}\)

1. 

a.\(\left(\frac{1}{2}\right)^2=\frac{1}{4}\)

b. \(\left(\frac{1}{2}\right)^3=\frac{1}{8}\)

c. \(\left(\frac{-3}{5}\right)^5=\frac{-243}{3125}\)

d. \(\left(\frac{-1}{5}\right)^2=\frac{1}{25}\)

e. \(\left(\frac{-1}{6}\right)^3=\frac{-1}{216}\)

Trả lời:

Bài 1: 

a, \(\left(\frac{1}{2}\right)^4=\frac{1^4}{2^4}=\frac{1}{16}\)

b, \(\left(\frac{1}{2}\right)^3=\frac{1^3}{2^3}=\frac{1}{8}\)

c, \(\left(\frac{-3}{5}\right)^2=\frac{\left(-3\right)^2}{5^2}=\frac{9}{25}\)

d, \(\left(\frac{-1}{5}\right)^2=\frac{\left(-1\right)^2}{5^2}=\frac{1}{25}\)

e, \(\left(\frac{-1}{6}\right)^3=\frac{\left(-1\right)^3}{6^3}=\frac{-1}{216}\)

Bài 2:

a, \(\left(\frac{3}{2}\right)^2.\left(\frac{4}{3}\right)^2=\frac{9}{4}.\frac{16}{9}=4\)

b, \(\left(-\frac{1}{2}\right)^3.\left(\frac{2}{3}\right)^3=-\frac{1}{8}.\frac{8}{27}=-\frac{1}{27}\)

c, \(\left(-\frac{1}{2}\right)^2.\left(\frac{2}{5}\right)^2=\frac{1}{4}.\frac{4}{25}=\frac{1}{25}\)

d, \(\left(-\frac{1}{2}\right)^3.\left(\frac{2}{3}\right)^3=-\frac{1}{8}.\frac{8}{27}=-\frac{1}{27}\)

e, \(\left(-5\right)^3.\frac{1}{5}=-125.\frac{1}{5}=-25\)

f, \(\left(\frac{2}{9}\right)^5.\left(-\frac{27}{4}\right)^5=\frac{2^5}{9^5}.\frac{\left(-27\right)^5}{4^5}=\frac{2^5.\left(-27\right)^5}{9^5.4^5}=\frac{2^5.\left[\left(-3\right)^3\right]^5}{\left(3^2\right)^5.\left(2^2\right)^5}=-\frac{2^5.3^{15}}{3^{10}.2^{10}}=\frac{3^5}{2^5}\)

\(\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+...+\frac{1}{197\times200}\)

\(=\frac{1}{3}\times\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+...+\frac{3}{197\times200}\right)\)

\(=\frac{1}{3}\times\left(\frac{8-5}{5\times8}+\frac{11-8}{8\times11}+\frac{14-11}{11\times14}+...+\frac{200-197}{197\times200}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{197}-\frac{1}{200}\right)\)

\(=\frac{1}{3}\times\left(\frac{1}{5}-\frac{1}{200}\right)\)

\(=\frac{13}{200}\)