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38 = 32 . 32 . 32 . 32
= 9 . 9 . 9 . 9
= 92 . 92
= 81 . 81
= 812
= 6561
24 = 2 . 2 . 2 . 2
= 22 . 22
= 4 . 4
= 42
= 16
\(3^2=3\cdot3=9\)
\(4^{10}=4.4.4.4.4.4.4.4.4.4=1048576\)
\(7^4=7\cdot7\cdot7\cdot7=2401\)
\(8^2=8\cdot8=64\)
Trả lời
(2+3)4.42= 54.42= 625.16=10000
52.22.4= 25.4.4=400
Học tốt. k mik nha
\(4^8.2^{20}.9^{12}.27^5.81^4.25^{20}.125^4\)
\(=\left(2^2\right)^8.2^{20}.\left(3^2\right)^{12}.\left(3^3\right)^5.\left(3^4\right)^4.\left(5^2\right)^{20}.\left(5^3\right)^4\)
\(=2^{16}.2^{20}.3^{15}.3^{16}.5^{40}.5^{12}\)
\(=2^{16+20}.3^{15+16}.5^{40+12}\)
\(=2^{36}.3^{31}.5^{52}\)
Vì 2 < 3 nên \(2^{2^2}\)< \(3^{2^2}\)
Dễ quá
Hiện tại mình bị mất ních nên các bạn ủng hộ nick này nhiều nha
\(2^{2^2}\)và \(3^{2^2}\)
Vì 2 < 3
Nên \(2^{2^2}< 3^{2^2}\)
........
1,
\(A=2^0+2^1+2^2+..+2^{2006}\)
\(=1+2+2^2+...+2^{2016}\)
\(2A=2+2^2+2^3+..+2^{2007}\)
\(2A-A=\left(2+2^2+2^3+..+2^{2007}\right)-\left(1+2+2^2+..+2^{2006}\right)\)
\(A=2^{2017}-1\)
\(B=1+3+3^2+..+3^{100}\)
\(3B=3+3^2+3^3+..+3^{101}\)
\(3B-B=\left(3+3^2+..+3^{101}\right)-\left(1+3+..+3^{100}\right)\)
\(2B=3^{101}-1\)
\(\Rightarrow B=\frac{3^{100}-1}{2}\)
\(D=1+5+5^2+...+5^{2000}\)
\(5D=5+5^2+5^3+...+5^{2001}\)
\(5D-D=\left(5+5^2+..+5^{2001}\right)-\left(1+5+...+5^{2000}\right)\)
\(4D=5^{2001}-1\)
\(D=\frac{5^{2001}-1}{4}\)
Trả lời :
a, \(3^6\text{ x }3^2+2\text{ x }81^2=3^8+2\text{ x }\left(3^4\right)^2=3^8+2\text{ x }3^8=\left(2+1\right)\text{ x }3^8=3\text{ x }3^8=3^9\)
b, \(\left(6^3\text{ x }8^4\right)\text{ : }12^3\)
\(=6^3\text{ x }8^4\text{ : }12^3\)
\(=\left(2\cdot3\right)^3\text{ x }\left(2^3\right)^4\text{ : }\left(2^2\cdot3\right)^3\)
\(=2^3\cdot3^3\text{ x }2^{12}\text{ : }\left(2^6\cdot3^3\right)\)
\(=2^3\cdot3^3\text{ x }2^{12}\text{ : }2^6\text{ : }3^3\)
\(=2^9\)
Câu c không hiểu đề !
a)
\(2^3=8\\ 2^4=16\\ 2^5=32\\2^6=64\\ 2^7=128\\ 2^8=256\\ 2^9=512\\ 2^{10}=1024 \)
b)
\(3^2=9\\3^3=27\\ 3^4=81\\ 3^5=243\)
c)
\(4^2=16\\ 4^3=64\\ 4^4=256\)
d)
\(5^2=25\\ 5^3=125\\ 5^4=625\)
e)
\(6^2=36\\ 6^3=216\\ 6^4=1296\)
Lời giải:
\(2^{27}.3^{18}=(2^3)^9.(3^2)^9=8^9.9^9=(8.9)^9=72^9\)
\(25^4.2^8=25^4.(2^2)^4=25^4.4^4=(25.4)^4=100^4\)
\((-9)^4.27^2=9^4.27^2=(3^2)^4.(3^3)^2=3^8.3^6=3^{8+6}=3^{14}\)
\(-5^4:25=-5^4:(5^2)=-5^{4-2}=-5^2\)
43 = 4.4.4 = 64