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) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

C

C

C

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

âm 9 nha bạn
 

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

xin lỗi bạn nha

mik ko viết được mũ nó lại thành ra thế này

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

XÉt vế trái: 45^10.5^30= 45^10. (5^3)^10=45^10.125^10=(45.125)^10=5625^10 (1)
XÉT vế phải : 75^20 = (75^2)^10 = 5625^101 (2)
Từ(1) và (2) => 45^10 . 5^30=75^20 (đpcm)

\(70-5\cdot\left(x-3\right)=45\)

\(\Rightarrow5\cdot\left(x-3\right)=70-45\)

\(\Rightarrow5\cdot\left(x-3\right)=25\)

\(\Rightarrow x-3=\dfrac{25}{5}\)

\(\Rightarrow x-3=5\)

\(\Rightarrow x=5+3=8\)

==============

\(10+2\cdot x=4^5:4^3\)

\(\Rightarrow10+2\cdot x=4^2\)

\(\Rightarrow10+2\cdot x=16\)

\(\Rightarrow2\cdot x=16-10\)

\(\Rightarrow2\cdot x=6\)

\(\Rightarrow x=\dfrac{6}{2}=3\)

=============

\(2\cdot x-138=2^3\cdot3^2\)

\(\Rightarrow2\cdot x-138=72\)

\(\Rightarrow2\cdot x=72+138\)

\(\Rightarrow2\cdot x=210\)

\(\Rightarrow x=\dfrac{210}{2}=105\)

==============

\(231-\left(x-6\right)=1339:12\)

\(\Rightarrow231-x+6=1339:12\)

\(\Rightarrow237-x=\dfrac{1339}{12}\)

\(\Rightarrow x=237-\dfrac{1339}{12}\)

\(\Rightarrow x=\dfrac{1505}{12}\)

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