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b) 32, 33, 34 , 35.
\(a,2^2=4,2^3=8,2^4=16,2^5=32,2^6=64,2^7=128,2^8=256,2^9=512,2^{10}=1024\)
\(b,3^2=9,3^3=27,3^4=81,3^5=243\)
\(c,4^2=16,4^3=64,4^4=256\)
\(d,5^2=25,5^3=125,5^4=625\)
2,
a) \(315-\left(135-x\right)=215\)
\(\Rightarrow135-x=315-215\)
\(\Rightarrow135-x=100\)
\(\Rightarrow x=135-100\)
\(\Rightarrow x=35\)
b) \(x-320:32=25\cdot16\)
\(\Rightarrow x-10=5^2\cdot4^2\)
\(\Rightarrow x-10=20^2\)
\(\Rightarrow x-10=400\)
\(\Rightarrow x=410\)
c) \(3\cdot x-2018:2=23\)
\(=3\cdot x-1009=23\)
\(\Rightarrow3\cdot x=1032\)
\(\Rightarrow x=1032:3\)
\(\Rightarrow x=344\)
d) \(280-9\cdot x-x=80\)
\(\Rightarrow280-x\cdot\left(9+1\right)=80\)
\(\Rightarrow280-10\cdot x=80\)
\(\Rightarrow10\cdot x=280-80\)
\(\Rightarrow10\cdot x=200\)
\(\Rightarrow x=20\)
e) \(38\cdot x-12\cdot x-x\cdot16=40\)
\(\Rightarrow x\cdot\left(38-12-16\right)=40\)
\(\Rightarrow x\cdot10=40\)
\(\Rightarrow x=40:10\)
\(\Rightarrow x=4\)
a,
= 51 - 2022 + 2022
= 51
b, = -2019 - 11 + 2019
= -11
c, = 27 - 52 - 37 + 52
= -10
d, = 19 - 32 + 41 - 19 + 25 - 41
= -7
a) \(4^8\cdot4^4=\left(2^2\right)^8\cdot\left(2^2\right)^4=2^{16}\cdot2^8=2^{16+8}=2^{24}\)
b) \(5^{12}\cdot7-5^{11}\cdot10\)
\(=5^{11}\cdot\left(5\cdot7-10\right)=5^{11}\cdot\left(35-10\right)=5^{11}\cdot25\)
\(=5^{11}\cdot5^2=5^{11+2}=5^{13}\)
d) \(27^{16}:9^{10}\)
\(=\left(3^3\right)^{16}:\left(3^2\right)^{10}=3^{48}:3^{20}=3^{48-20}=3^{28}\)
e) \(125^3:25^4=\left(5^3\right)^3:\left(5^2\right)^4=5^9:5^8=5^{9-8}=5\)
f) \(24^4:3^4-32^{12}:16^{12}\)
\(=\left(24:4\right)^4-\left(32:16\right)^{12}\)
\(=6^4-2^{12}\)
\(=2^4\cdot\left(3^4-2^8\right)=2^4\cdot-175=-2800\)
A = \(\dfrac{18}{26}\) + (-\(\dfrac{5}{27}\)) + (-\(\dfrac{22}{86}\)) + \(\dfrac{12}{39}\) - \(\dfrac{32}{43}\)
A = \(\dfrac{9}{13}\) - \(\dfrac{5}{27}\) - \(\dfrac{11}{43}\) + \(\dfrac{4}{13}\) - \(\dfrac{32}{43}\)
A = (\(\dfrac{9}{13}\) + \(\dfrac{4}{13}\)) - (\(\dfrac{11}{43}\) + \(\dfrac{32}{43}\)) - \(\dfrac{5}{27}\)
A = \(\dfrac{13}{13}\) - \(\dfrac{43}{43}\) - \(\dfrac{5}{27}\)
A = 1 - 1 - \(\dfrac{5}{27}\)
A = 0 - \(\dfrac{5}{27}\)
A = - \(\dfrac{5}{27}\)
a) A = 2000 . 2000 = ( 1990 + 10 ) . 2000
= 1990 . 2000 + 10 . 2000
B = 1990 . 2010 = 1990 . ( 2000 + 10 )
= 1990 . 2000 + 1990 . 10
Vì 10 . 2000 > 1990 . 10 nên A > B
A lớn hơn B là: ( 10 . 2000 ) - ( 1990 . 10 ) = 20000 - 19900 = 100
b) A = 25 . 33 - 10 = 25 . ( 31 + 2 ) - 10
= 25 . 31 + 25 . 2 - 10
= 25 . 31 + ( 25 . 2 - 10 )
= 25 . 31 + 40
B = 31 . 26 + 10
= 31 . ( 25 + 1) + 10
= 31 . 25 + 35 + 10
= 31 . 25 + ( 35 + 10 )
= 31 . 25 + 45
Vì 45 > 40 nên B > A
B lớn hơn A là : 45 - 40 = 10
c) A = 32 . 53 - 31
= ( 31 + 1 ) . 53 - 31
= 31 . 53 + 53 - 31
= 31 . 53 + ( 53 - 31 )
= 31 . 53 + 22
Vì 32 > 22 nên B > A
A= 27 : 25 + 10
A = 27-5 + 10
A = 22 + 10
A = 4 + 10
A = 14
B = 32. 33 - 32. 43
B = 9. 27 - 9. 64
B = 9. ( 27 - 64 )
B = 9. -37
B = -333
C = 52020: 52022 + 30 + 1
C = 52020-2022 + 1 + 1
C = 5-2 + 1 + 1
C = \(\dfrac{1}{25}+1+1\)
\(C=0,04+1+1\)
C = 2,04
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