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a) \(2^3.3^2=8.9=72\)
b) \(5^{10}:5^7=5^2=25\)
c) \(2^6:2=2^5=32\)
d) \(7^4:7^4=7^0=1\)
e) \(9^5:9^5=9^0=1\)
Bài 1:
a) 02002 < 02023
b) 20220 = 20230
c) 549 < 5510
d) ( 4 + 5 )3 > 42 + 52
đ) 92 - 32 > ( 9 - 3 )2
Bài 2:
a) 32 x 43 - 32 + 333
= 9 x 64 - 9 + 333
= 576 - 9 + 333
= 567 + 333
= 900
b) 5 x 43 + 24 x 5 + 410
= 5 x 64 + 24 x 5 + 1
= 5 x ( 64 + 24 ) + 1
= 5 x 88 + 1
= 440 + 1
= 441
c) 23 x 42 + 32 x 5 - 40 x 12023
= 8 x 16 + 9 x 5 - 40 x 1
= 128 + 45 - 40
= 133
Bài 1 :
a) \(0^{2002}=0;0^{2023}=0\Rightarrow0^{2002}=0^{2023}\)
b) \(2022^0=1;2023^0=1\Rightarrow2022^0=2023^0\)
c) \(54^9< 55^9;55^9< 55^{10}\Rightarrow54^9< 55^{10}\)
d) \(\left(4+5\right)^3>\left(4+5\right)^2;\left(4+5\right)^2>4^2+5^2\Rightarrow\left(4+5\right)^3>4^2+5^2\)
đ) \(9^2-3^2=81-9=82;\left(9-3\right)^2=6^2=36\Rightarrow9^2-3^2>\left(9-3\right)^2\)
a,( 393+390) : (317. 373)
= (33+1). 390 : 390
= 33+1
=27+1
=28
b,(556+57) : (549+1)
=57. (549+1) : (549+1)
=57= 78125
c,(722+721+720) ; (25+24+32)
= 720. (72+71+1) : [24. (2+1)+32 ]
= 720. 57 : [ 24. 3 +32 ]
= 720. 57 : ( 24+3) . 3
= 720. 57 : 19 . 3
= 720. 57 : 57
= 720
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. a) 4.415.8.25.125
= (4.25). (8.125).415
= 100.1000.415
= 100000.415
= 41500000
b) 2.31.12+4.42.6+8.27.3
= (2.31.12)+(4.42.6)+(8.27.3)
= (2.12).31+(4.6).42+(8.3).27
= 24.31+24.42+24.27
= 24 (31+42+27)
= 24.100
= 2400
b)\(3.4^2-2.3=3.\left(4^2-3\right)\)
\(=3.13\)
\(=39\)
Học tốt nha!!!
a) 23 = 8; 24 = 16; 25 = 32; 26 = 64; 27 = 128; 28 = 256; 29 = 512; 210 = 1024
b) 32 = 9; 33 = 27; 34 = 81; 35 = 243
c) 42 = 16; 43 = 64; 44 = 256
d) 52 = 25; 53 = 125; 54 = 625
c) 62 = 36; 63 = 216; 64 = 1296
a) 23 = 8; 24 = 16; 25 = 32; 26 = 64; 27 = 128; 28 = 256; 29 = 512; 210 = 1024
b) 32 = 9; 33 = 27; 34 = 81; 35 = 243
c) 42 = 16; 43 = 64; 44 = 256
d) 52 = 25; 53 = 125; 54 = 625
e) 62 = 36; 63 = 216; 64 = 1296
HT
d: Ta có: \(D=5^3+6^3+59\)
\(=125+216+59\)
\(=400=20^2\)
`A = 2 + 2^2+ ... + 2^2017`
`=> 2A = 2^2 + 2^3 + ... + 2^2018`
`=> 2A - A = (2^2 + 2^3 + ... + 2^2018) - (2 + 2^2 + ... +2^2017)`
`=> A = 2^2018 - 2`
`B = 1 + 3^2 + ... + 3^2018`
`=> 3^2B = 3^2 + 3^4 + ... + 3^2020`
`=> 9B-B =(3^2 + 3^4 + ... + 3^2020) - (1 + 3^2 + ... + 3^2018`
`=> 8B = 3^2020 - 1`
`=> B = (3^2020 - 1)/8`
`C = 5 + 5^2 - 5^3 + ... + 5^2018`
`=> 5C = 5^2 + 5^3 - 5^4 + ... +5^2019`
`=> 5C + C = ( 5^2 + 5^3 - 5^4 + ... 5^2019) + (5 + 5^2 - 5^3 + ... + 5^2018)`
`=> 6C = 55 + 5^2019`
`=> C = (5^2019 + 55)/6`