2:

a: \(2^2\cdot3-4=4\cdot3-4=12-4=8\)

b: \(16-2^3\cdot2=16-2^4=16-16=0\)

c: \(4^2-4\cdot2=16-8=8\)

d: \(3^3-2\cdot3^2=27-2\cdot9=27-18=9\)

e: \(7^2-9\cdot2^2=49-9\cdot4=49-36=13\)

f: \(2^2\cdot3+4^2=4\cdot3+16=12+16=28\)

Bài 1:

a: \(13+21\cdot5-\left(198:11-8\right)\)

\(=13+105-18+8\)

=21+87

=108

b: \(272:16-5+4\cdot\left(30-5-255:17\right)\)

\(=17-5+4\cdot\left(30-5-15\right)\)

\(=12+4\cdot10=12+40=52\)

c: \(15\cdot24-14\cdot5\cdot\left(145:5-27\right)\)

\(=360-70\left(29-27\right)\)

=360-140

=220

d: \(18\cdot3-18\cdot2+3\cdot\left(\dfrac{51}{17}\right)\)

\(=18\left(3-2\right)+3\cdot3\)

=18+9

=27

e: \(64+115+36-25\cdot8\cdot6\cdot2^2\cdot3+4^2\)

\(=100+115-200\cdot6\cdot4\cdot3+16\)

\(=231-14400=-14169\)

f: \(15\cdot8-\left(17-30+83\right)-144:6\)

\(=120-24-\left(100-30\right)\)

=96-70

=26

a) \(\dfrac{2}{5}-\dfrac{3}{15}\)

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

\(=\dfrac{2}{5}-\dfrac{1}{5}\)

\(=\dfrac{1}{5}\)

b) \(\dfrac{9}{27}-\dfrac{2}{9}\)

\(=\dfrac{9:3}{27:3}-\dfrac{2}{9}\)

\(=\dfrac{3}{9}-\dfrac{2}{9}\)

\(=\dfrac{1}{9}\)

c) \(\dfrac{18}{24}-\dfrac{4}{8}\)

\(=\dfrac{18:6}{24:6}-\dfrac{4:2}{8:2}\)

\(=\dfrac{3}{4}-\dfrac{2}{4}\)

\(=\dfrac{1}{4}\)

d) \(\dfrac{6}{16}-\dfrac{10}{64}\)

\(=\dfrac{6\times2}{16\times2}-\dfrac{10:2}{64:2}\)

\(=\dfrac{12}{32}-\dfrac{5}{32}\)

\(=\dfrac{7}{32}\)

a: \(\dfrac{3}{9}\times\dfrac{5}{4}=\dfrac{5}{4}\times\dfrac{1}{3}=\dfrac{5\times1}{4\times3}=\dfrac{5}{12}\)

b: \(\dfrac{10}{15}\times\dfrac{3}{5}=\dfrac{3}{5}\times\dfrac{2}{3}=\dfrac{3\times2}{5\times3}=\dfrac{2}{5}\)

c: \(\dfrac{5}{8}\times\dfrac{4}{12}=\dfrac{5}{8}\times\dfrac{1}{3}=\dfrac{5}{3\times8}=\dfrac{5}{24}\)

d: \(\dfrac{9}{27}\times\dfrac{3}{21}=\dfrac{1}{7}\times\dfrac{1}{3}=\dfrac{1\times1}{7\times3}=\dfrac{1}{21}\)

a: \(\dfrac{1}{8}\cdot\dfrac{4}{5}:\dfrac{3}{5}=\dfrac{1}{10}\cdot\dfrac{5}{3}=\dfrac{1}{2\cdot3}=\dfrac{1}{6}\)

b: \(=\dfrac{8-3}{12}\cdot\dfrac{6}{5}=\dfrac{6}{12}=\dfrac{1}{2}\)

c: \(=\dfrac{24}{35}:\dfrac{32}{35}=\dfrac{3}{4}\)

d: =63/21+15/21-7/21=71/21

a \(\dfrac{1}{8}\times\dfrac{4}{5}\times\dfrac{10}{6}=\dfrac{1}{6}\)

b \(\left(\dfrac{8}{12}-\dfrac{3}{12}\right)\times\dfrac{6}{5}=\dfrac{5}{12}\times\dfrac{6}{5}=\dfrac{1}{2}\)

c \(\dfrac{24}{35}:\dfrac{32}{35}=\dfrac{24}{35}\times\dfrac{35}{32}=\dfrac{3}{4}\)

d \(\dfrac{63}{21}+\dfrac{15}{21}-\dfrac{7}{21}=\dfrac{71}{21}\)

a: \(\dfrac{16}{15}\cdot\dfrac{-5}{14}\cdot\dfrac{54}{24}\cdot\dfrac{56}{21}\)

\(=\dfrac{16}{24}\cdot\dfrac{-5}{15}\cdot\dfrac{54}{21}\cdot\dfrac{56}{14}\)

\(=\dfrac{2}{3}\cdot\dfrac{-1}{3}\cdot\dfrac{18}{7}\cdot4\)

\(=\dfrac{-2\cdot2\cdot4}{7}=-\dfrac{16}{7}\)

b: \(\dfrac{7}{3}\cdot\dfrac{-5}{2}\cdot\dfrac{15}{21}\cdot\dfrac{4}{-5}\)

\(=\dfrac{7}{3}\cdot\dfrac{5}{7}\cdot\dfrac{5}{2}\cdot\dfrac{4}{5}\)

\(=\dfrac{5}{3}\cdot\dfrac{4}{2}=\dfrac{5}{3}\cdot2=\dfrac{10}{3}\)

c: \(\left(-\dfrac{2}{5}+\dfrac{1}{3}\right)\left(\dfrac{3}{2}-\dfrac{3}{7}\right)\)

\(=\dfrac{-2\cdot5+3}{15}\cdot\dfrac{3\cdot7-3\cdot2}{14}\)

\(=\dfrac{-7}{15}\cdot\dfrac{15}{14}=\dfrac{-7}{14}=-\dfrac{1}{2}\)

d: \(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\left(5-\dfrac{1}{4}\right)\)

\(=\dfrac{3-2}{6}\cdot\dfrac{20-1}{4}\)

\(=\dfrac{1}{6}\cdot\dfrac{19}{4}=\dfrac{19}{24}\)

e: \(\left(\dfrac{4}{5}\right)^2=\dfrac{4^2}{5^2}=\dfrac{16}{25}\)

a) 2 giờ 27 phút + 3 giờ 18 phút =   5 giờ 45 phút

b) 5 ngày 15 giờ + 4 ngày 12 giờ = 9 ngày 27 giờ

c) 15 phút 36 giây +11 phút 24 giây = 26 phút 50 giây

2:

a: A=1+2+2^2+2^3+2^4

=>2A=2+2^2+2^3+2^4+2^5

=>A=2^5-1

=>A=B

b: C=3+3^2+...+3^100

=>3C=3^2+3^3+...+3^101

=>2C=3^101-3

=>\(C=\dfrac{3^{101}-3}{2}\)

=>C=D

Ta có: 

\(\left\{\begin{matrix}5^{27}=\left(5^3\right)^9=125^9\\2^{63}=\left(2^7\right)^9=128^9\end{matrix}\right\}\Rightarrow5^{27}< 2^{63}\left(1\right)\)

\(\left\{\begin{matrix}2^{63}=\left(2^9\right)^7=512^7\\5^{28}=\left(5^4\right)^7=625^7\end{matrix}\right\}\Rightarrow2^{63}< 5^{28}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow5^{27}< 2^{63}< 5^{28}\) (đpcm)

 \(a.5^{27}=\left(5^3\right)^9=125^9\\ 2^{63}=\left(2^7\right)^9=128^9\)

Vì 128⁹ > 125⁹ => 2⁶³ > 5²⁷

^{\(5^{28}=\left(5^4\right)^7=625^7\\ 2^{63}=\left(2^9\right)^7=512^7\)}

Vì 625⁷ > 512⁷ = > 5²⁸ > 2⁶³

Đã CMR: \(5^{27}< 2^{63}< 5^{28}\)

\(b.A=1+2+2^2+2^3+2^4\\ 2A=2+2^2+2^3+2^4+2^5\\ 2A-A=\left(2+2^2+2^3+2^4+2^5\right)-\left(1+2+2^2+2^3+2^4+\right)\\ A=2^5-1\\ 2^5-1=2^5-1=>A=B\\ c,C=3+3^2+....+3^{100}\\ 3C=3^2+......+3^{101}\\ 3C-C=\left(3^2+...+3^{101}\right)-\left(3+...+3^{100}\right)\\ 2C=3^{101}-3\\ C=\dfrac{3^{101}-3}{2}\\ \dfrac{3^{101}-3}{2}=\dfrac{3^{101}-3}{2}=>C=D\)