Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

\(\left(1\right)=1^3=1\)

1: \(78+22+18\)

\(=\left(78+22\right)+18\)

=100+18

=118

2: \(94+563+\left(106-563\right)-\left(-70\right)\)

\(=94+563+106-563+70\)

\(=\left(94+106\right)-\left(563-563\right)+70\)

=100-0+70

=170

3: \(25\cdot154-25+47\cdot25\)

\(=25\left(154-1+47\right)\)

\(=25\cdot200=5000\)

4: \(\left[5^{29}+5^{30}\left(16-11\right)\right]:5^{29}\)

\(=\left(5^{29}+5^{30}\cdot5\right):5^{29}\)

\(=\dfrac{5^{29}\cdot1+5^{29}\cdot5^2}{5^{29}}\)

\(=1+5^2=26\)

8: \(25\cdot2^3-\left(9-14\right)+\left(29-34+20\right)\)

\(=25\cdot8-\left(-5\right)+\left(-5\right)+20\)

\(=200+5-5+20\)

=220

\(a,3^6:3^5=3^{6-5}=3\\ b,5^7:5^5=5^{7-5}=5^2=25\\ c,14^5:2^3:7^4=\left(2^5:2^3\right)\cdot\left(7^5:7^4\right)=2^2\cdot7=28\\ d,5^4-2\cdot5^3=5^3\left(5-2\right)=3\cdot5^3=375\)

a) 3^6 : 3^5 = 729 : 243 = 3

b) 5^7 : 5^5 = 78125 : 3125 = 25

c) 14^5 : 2^3 : 7^4 = 537824 : 8 : 2401 = 89

d) 5^4 - 2 * 5^3 = 625 - 2 * 125 = 625 - 250 = 375

\(a,3^6:3^5=3^{6-5}=3^1=3\\ b,5^7:5^5=5^{7-5}=5^2=25\\ c,14^5:2^3:7^4=\left(2^5:2^3\right).\left(7^5:7^4\right)=2^{5-3}.7^{5-4}=2^2.7^1=4.7=28\\ d,5^4-2.5^3=5.5^3-2.5^3=\left(5-2\right).5^3=3.5^3=3.125=375\)

a: \(=32-76=-44\)

b: \(=20-30+4^2=-10+16=6\)

h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)

\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)

g, \(x^4-2x^2+1=\left(x^2-1\right)^2\)

\(\Rightarrow\left(x^4-2x^2+1\right):\left(1-x^2\right)\\ =\left(x^2-1\right)^2:\left(1-x^2\right)\\ =x^2-1\)

a) 2^4 * 38 - 2^4 * 37 = 16 * 38 - 16 * 37 = 608 - 592 = 16

b) 4^2 * 444446 - 4^3 * 111111 = 16 * 444446 - 64 * 111111 = 7107136 - 7106944 = 192

c) (2^9 * 3 + 2^9 * 5) / 2^12 = (512 * 3 + 512 * 5) / 4096 = (1536 + 2560) / 4096 = 4096 / 4096 = 1

d) 13^2 - (5^2 * 4 + 2^2 * 15) = 169 - (25 * 4 + 4 * 15) = 169 - (100 + 60) = 169 - 160 = 9

đề cô em ra sao thì em viết v thôi

\(a,2^4.38-2^4.37=2^4.\left(38-37\right)=2^4.1=16\\ b,4^2.444446-4^3.111111\\ =4^2.\left(444446-4.111111\right)\\ =4^2.2=16.2=32\\ c,\left(2^9.3+2^9.5\right):2^{12}\\ =2^9.\left(3+5\right):2^{12}=2^9.8:2^{12}=2^9.2^3:2^{12}=2^{9+3-12}=2^0=1\\ d,13^2-\left(5^2.4+2^4.15\right)=13^2-5.4.\left(5+4.3\right)\\ =169-20.17\\ =169-340=-171\)

Giúp mink vs ~

a) \(\frac{4}{3}-\frac{2}{5}\)

\(=\frac{20}{15}-\frac{6}{15}=\frac{14}{15}\)

b) \(\left|-\frac{1}{10}\right|-\left(-\frac{1}{3}\right)^2\div\frac{5}{9}\)

\(=\frac{1}{10}-\frac{1}{9}\cdot\frac{9}{5}\)

\(=\frac{1}{10}-\frac{1}{5}=\frac{1}{10}-\frac{2}{10}\)

\(=-\frac{1}{10}\)

c) Đề bài có vấn đề!!!

d) \(\left(-0,2\right)^2\cdot5-8^2\cdot\frac{9^4}{3^7}\cdot4^3\)

\(=0,04\cdot5-64\cdot\frac{\left(3^2\right)^4}{3^7}\cdot64\)

\(=0,2-4096\cdot\frac{3^8}{3^7}=0,2-4096\cdot3\)

\(=0,2-12288=-128878\)