Chung minh rang
128 . 9 12= 1816
75 20 = 4510 . 530
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Bài 8:
a) \(2^{225}=\left(2^3\right)^{75}=8^{75}\)
\(3^{150}=\left(3^2\right)^{75}=9^{75}\)
Vì \(8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)
b) \(2^{91}=\left(2^{13}\right)^7=8192^7\)
\(5^{35}=\left(5^5\right)^7=3125^7\)
Vì \(8192^7>3125^7\Rightarrow2^{91}>5^{35}\)
c) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)
12) 17 – 11 – 14 – (-39)
=17-11-14+39
=6-14+39
=-8+39
=31
13) −127 - 18.( 5 - 6)
=-127-18.1
=-145
14) 100 + (+430) + 2145 + (-530)
=530+2145-530
=(530-530)+2145
=0+2145
=2145
15) (+12).13 + 13.(-22)
=13.[12+(-22)]
=13.(-10)
=-130
16) {[14 : (-2)] + 7} : 2012
={-7+7}:2012
=0:2012
=0
17) 13 – 18 – (- 42) - 15
=13-18+42-15
=-5+42-15
=37-15
=22
18) 369 – 4[(-5) + 4.(-8)]
=369-4[-5+(-32)]
=369-4(-37)
=369+148
=517
19) (-12).(-13) +13.(-29)
=12.13+13.(-29)=13.[12+(-29)]=13.(-17)=-221
20) 125 – 4[ 3 – 7.(-2) ]
=125-4[3+14]
=125-4.17
=125-68
=57
21) (-14).9 – 13.(-9)
=(-14).9+13.9
=9.[-14+13]
=9.(-1)
=-9
a, 128.912=(22.3)8.912=(22)8.38.912=216.(32)4.912=216.94.912=216.916=(2.9)16=1816128.912=(22.3)8.912=(22)8.38.912=216.(32)4.912=216.94.912=216.916=(2.9)16=1816,b, 4510.530=(32.5)10.530=320.510.530=320.540=320.(52)20=320.2520=(3.25)20=75204510.530=(32.5)10.530=320.510.530=320.540=320.(52)20=320.2520=(3.25)20=7520
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128.912=(22.3)8.912=(22)8.38.912=216.(32)4.912=216.94.912=216.916=(2.9)16=1816
b, 4510.530=(32.5)10.530=320.510.530=320.540=320.(52)20=320.2520=(3.25)20=75204510.530=(32.5)10.530=320.510.530=320.540=320.(52)20=320.2520=(3.25)20=7520
128.912=(22.3)8.912=(22)8.38.912=216.(32)4.912=216.94.912=216.916=(2.9)16=1816
\(70-5\cdot\left(x-3\right)=45\)
\(\Rightarrow5\cdot\left(x-3\right)=70-45\)
\(\Rightarrow5\cdot\left(x-3\right)=25\)
\(\Rightarrow x-3=\dfrac{25}{5}\)
\(\Rightarrow x-3=5\)
\(\Rightarrow x=5+3=8\)
==============
\(10+2\cdot x=4^5:4^3\)
\(\Rightarrow10+2\cdot x=4^2\)
\(\Rightarrow10+2\cdot x=16\)
\(\Rightarrow2\cdot x=16-10\)
\(\Rightarrow2\cdot x=6\)
\(\Rightarrow x=\dfrac{6}{2}=3\)
=============
\(2\cdot x-138=2^3\cdot3^2\)
\(\Rightarrow2\cdot x-138=72\)
\(\Rightarrow2\cdot x=72+138\)
\(\Rightarrow2\cdot x=210\)
\(\Rightarrow x=\dfrac{210}{2}=105\)
==============
\(231-\left(x-6\right)=1339:12\)
\(\Rightarrow231-x+6=1339:12\)
\(\Rightarrow237-x=\dfrac{1339}{12}\)
\(\Rightarrow x=237-\dfrac{1339}{12}\)
\(\Rightarrow x=\dfrac{1505}{12}\)
b: \(8^{12}-2^{33}-2^{30}\)
\(=2^{36}-2^{33}-2^{30}\)
\(=2^{30}\left(2^6-2^3-1\right)=2^{30}\cdot55⋮55\)
c: \(8^7-2^{18}=2^{21}-2^{18}\)
\(=2^{18}\left(2^3-1\right)=2^{17}\cdot14⋮14\)
d: \(10^6-5^7\)
\(=2^6\cdot5^6-5^7\)
\(=5^6\left(2^6-5\right)=5^6\cdot59⋮59\)
Phân số không bằng phân số nào trong các phân số còn lại là − 4 − 9