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a) $3^8:3^6=3^{8-6}=3^2$
$19^7:19^3=19^{7-3}=19^4$
$2^{10}:8^3=2^{10}:(2^3)^3=2^{10}:2^9=2^{10-9}=2^1$
$12^7:6^7=(12:6)^7=2^7$
$27^5:81^3=(3^3)^5:(3^4)^3=3^{15}:3^{12}=3^{15-12}=3^3$
b) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
1) 56 63 . 3 . 2
23 . 32. 100.103
2) lay may tinh bam nha ban.
:-) k nha
1)
a) 5 . 5 . 5 . 5 . 5 . 5 = 56
b) 6 . 6 . 6 . 3 . 2 = 6 . 6 . 6 . 6 = 64
c) 2 . 2 . 2 . 3 . 3 = 23 . 32
d) 100 . 10 . 10 . 10 = 10 . 10 . 10 . 10 . 10 = 105
2)
a) 23 = 2 . 2 . 2 = 8
24 = 2 . 2 . 2 . 2 = 16
25 = 2 . 2 . 2 . 2 . 2 = 32
26 = 2 . 2 . 2 . 2 . 2 . 2 = 64
27 = 2 . 2 . 2 . 2 . 2 . 2 . 2 = 128
28 = 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 = 256
29 = 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 = 512
210 = 2 . 2 . 2 . 2 . 2. . 2 . 2 . 2 . 2 . 2 = 1024
b) 32 = 3 . 3 = 9
33 = 3 . 3 . 3. = 27
34 = 3 . 3 . 3 . 3 = 81
35 = 3 . 3 . 3 . 3 . 3 = 243
c) 42 = 4 . 4 = 16
43 = 4 . 4 . 4 = 64
44 = 4 . 4 . 4 . 4 = 256
d) 52 = 5 . 5 = 25
53 = 5 . 5 . 5 = 125
54 = 5 . 5 . 5 . 5 = 625
e) 62 = 6 . 6 = 36
63 = 6 . 6 . 6 = 216
64 = 6 . 6 . 6 . 6 = 1296
1 So sánh các lũy thừa
a) 912 và 277
Ta có : 912 = (32)12 = 32.12 = 324
277 = (33)7 = 33.7 = 321
Vì 24 > 21 nên 324 > 321 nên 912 > 277
b) 12580 và 25118
Ta có : 12580 = (53)80 = 53.80 = 5240
25118 = (52)118 = 52.118 = 5236
240 > 236 nên 5240 > 5236 nên 12580 > 25118
c) 1030 và 2100
Ta có : 1030 = 103. 10 = (103)10 = 100010
2100 = 210.10 = (210)10 = 102410
Vì 1000 < 1024 nên 1030 < 2100
\(a,213=200+10+3\)\(=\left(2x10^2\right)\)\(+10^1\)\(+\left(3x10^0\right)\)
\(b,421=400+20+1\)\(=\left(4x10^2\right)\)\(+\left(2x10^1\right)\)\(+10^0\)
\(c,1256=1000+200+50+6\)\(=10^3\)\(+\left(2x10^2\right)\)\(+\left(5x10^1\right)\)\(+\left(6x10^0\right)\)
\(d,2006=2000+6\)\(=\left(2x10^3\right)\)\(+\left(6x10^0\right)\)
\(e,abc=100a+10b+c=10^2\)\(a+10^1\)\(b+\left(cx10^0\right)\)
\(g,abcde=10000a+1000b+100c+10d+e\)\(=10^4\)\(a+10^3\)\(b+10^2\)\(c+10^1\)\(d+e\)
Bài 9: Viết các số sau dưới dạng tổn các lũy thừa của 10
a) 213 = 2 . 100 + 1 . 10 + 3 . 1 = 2 . 102 + 2 . 101 + 3 . 100
b) 421 = 4 . 100 + 2 . 10 + 1 . 1 = 4 . 102 + 2 . 101 + 1 . 100
c) 1256 = 1 . 1000 + 2 . 100 + 5 . 10 + 6 . 1 = 1 . 103 + 2 . 102 + 5 . 101 + 6 . 100
d) 2006 = 2 . 1000 + 6 . 1 = 2 . 103 + 1 . 100
e) abc = a . 100 + b . 10 + c . 1 = a . 102 + b . 101 + c . 100
g) abcde = a . 10000 + b . 1000 + c . 100 + d . 10 + e . 1 = a . 104 + b . 103 + c .102 + d . 101 + e . 100
Bài 10: Viết mỗi thương sau dưới dạng 1 lũy thừa
a) 38 : 36 = 32
75 : 72 = 73
197 : 193 = 194
210 : 83 = 210 : ( 23 )3 = 210 : 29 = 21 = 2
127 : 67 = ( 12 : 6 )7 = 27
275 : 813 = ( 33 )5 : ( 34 )3 = 315 : 312 = 33
b) 106 : 10 = 105
58 : 252 = 58 : ( 52 )2 = 58 : 54 = 54
49 : 642 = 49 : ( 43 )2 = 49 : 46 = 43
225 : 324 = 225 : ( 25 )4 = 225 : 220 = 5
183 : 93 = ( 18 : 9 )3 = 23
1253 : 254 = ( 53 )3 : ( 52 )4 = 59 : 58 = 5
1. A - B = 40+ 3/8 + 7/82 + 5/83 + 32/85 - (24/82 + 40+ 5/82 + 40/84 + 5/84 )
= 40.85/85 + 3.84/85 + 7.83/85 + 5.82/85 + 32/85 - 24.83/85 - 40.85/85 - 5.83/85 - 40.8/85 - 5.8/85
= 40.85/85 + 24.83/85 + 7.83/85 + 5.82/85 + 32/85 - 24.83/85 - 40.85/85 - 5.83/85 - 40.8/85 - 5.8/85
= 7.83/85 + 5.82/85 + 32/85 - 5.83/85 - 40.8/85 - 5.8/85
= 7.83/85 + 5.82/85 -8/85 - 5.83/85 - 40.8/85
= 2.83/85 + 5.82/85 - 40.8/85 - 8/85
= 2.83/85 + 40.8/85 - 40.8/85 - 8/85
= 2.83/85 - 8/85 > 0
Vay A > B
a/ \(9^{27}=\left(3^2\right)^{27}=3^{54}\) và \(81^{13}=\left(3^4\right)^{13}=3^{52}\Rightarrow3^{54}>3^{52}\Rightarrow9^{27}>81^{13}\)
b/ \(5^{14}=\left(5^2\right)^7=25^7< 27^7\)
d/ \(2^{300}=\left(2^3\right)^{100}=8^{100}\) và \(3^{200}=\left(3^2\right)^{100}=9^{100}\Rightarrow8^{100}< 9^{100}\Rightarrow2^{300}< 3^{200}\)
f/ \(3^{450}=\left(3^3\right)^{150}=27^{150}\) và \(5^{300}=\left(5^2\right)^{150}=25^{150}\Rightarrow27^{150}>25^{150}\Rightarrow3^{450}>5^{300}\)
c/ \(10^{30}=\left(10^3\right)^{10}=1000^{10}\) và \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\Rightarrow1000^{10}< 1024^{10}\Rightarrow10^{30}< 2^{100}\)
a) 37:35= 32
b)46 :46= 40
C) a4 : a= a3
d) 98:32 =314
e) 85:23 = 212
f) 37:27 = 34
\(a,3^7:3^5=3^2\)
\(b,4^6:4^6=4^0\)
\(c,a^4:a=a^3\)
\(d,9^8:3^2=9^4\)
\(e,8^5:2^3=8^{-7}\)
\(f,3^7:27=3^4\)
1,
a, \(11.11.11=11^3\)
b,\(55.5.5.13.13=55.5^2.13^2\)
c, \(3^7.3^{10}.3^2=3^{\left(7+10+2\right)}=3^{19}\)
d, \(2^5.2^6.2^7.2.2.2=2^5.2^6.2^7.2^3\)
e, \(2^9:2^3.2^4=2^6.2^4=2^{10}\)
2,
\(4^9:8^5=8\)
\(32^{10}:8^5=4^{10}.8^{10}:8^5=4^{10}.8^5\)
\(9^{15}:27^{10}=9^{15}:9^{10}.3^{10}=9^5.3^{10}\)( tự tính)
3,
Ta có:
\(7^{200}=7^{2.100}=\left(7^2\right)^{100}=49^{100}\)
\(2^{700}=2^{7.100}=\left(2^7\right)^{100}=128^{100}\)
Vì \(128^{100}>49^{100}\)nên \(2^{700}>7^{200}\)