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a)
49:44=45
178:175=173
210:82=210:24=26
1810:310=1510
275:813=315:312=33
b)106:102=104
59:56=53
410:643=4
225:324=225:220=25
184:94=94
\(4^9:4^4\)
=\(4^{9-4}\)
=\(4^5\)
\(17^8:17^5\)
=\(17^{8-5}\)
= \(17^3\)
\(2^{10}:8^2\)
\(=2^{^{ }10}:\left(2^3\right)^2\)
=\(2^{10}:2^6\)
\(=2^4\)
\(18^{10}:3^{10}\)
=\(\left(18:3\right)^{10}\)
=\(6^{10}\)
a)\(213=10^2+10^2+10^1+10^0+10^0+10^0\)
b)\(421=10^2+10^2+10^2+10^2+10^1+10^1+10^0\)
a) \(4^9:4^4\)
\(=4^{9-4}\)
\(=4^5\)
b) \(17^8:17^5\)
\(=17^{8-5}\)
\(=17^3\)
c) \(2^{10}:8^2\)
\(=2^{10}:\left(2^3\right)^2\)
\(=2^{10-6}\)
\(=2^4\)
d) \(18^{10}:3^{10}\)
\(=\left(18:3\right)^{10}\)
\(=6^{10}\)
e) \(27^5:81^3\)
\(=\left(3^3\right)^5:\left(3^4\right)^3\)
\(=3^{15}:3^{12}\)
\(=3^{15-12}\)
\(=3^3\)
f) \(10^6:100\)
\(=10^6:10^2\)
\(=10^{6-2}\)
\(=10^4\)
g) \(5^9:25^3\)
\(=5^9:\left(5^2\right)^3\)
\(=5^9:5^6\)
\(=5^{9-6}\)
\(=5^3\)
h) \(4^{10}:64^3\)
\(=4^{10}:\left(4^3\right)^3\)
\(=4^{10-9}\)
\(=4\)
i) \(2^{25}:32^4:18^4:9^4\)
\(=\left(2^{25}:2^{20}\right):\left(18^4\cdot9^4\right)\)
\(=2^5:9^8:2^4\)
\(=2:9^8\)
\(=\dfrac{2}{9^8}\)
a﴿ 213 = 200 + 10 + 3 = 2.100 + 10 + 3 = 2.10^ 2 + 10^ 1 + 3
b﴿ 421 = 400 + 20 + 1 = 4.100 + 2.10 + 1 = 4.10^ 2+ 2.10^ 1 + 1
c﴿ 2009 = 2000 + 9 = 2 . 1000 + 9 = 2.10 ^3 + 9
d﴿ abc = a.100 + b.10 + c = a.10^ 2 + b.10^ 1 + c
e﴿ abcde = a.10000 + b.1000 + c.100 + d.10 + e = a.10^ 4+ b.10^ 3+ c.10 ^2+ d.10^ 1 + e
a﴿ 213 = 200 + 10 + 3 = 2.100 + 10 + 3 = 2.10 2 + 10 1 + 3
b﴿ 421 = 400 + 20 + 1 = 4.100 + 2.10 + 1 = 4.10 2+ 2.10 1 + 1
c﴿ 2009 = 2000 + 9 = 2 . 1000 + 9 = 2.10 3 + 9
d﴿ abc = a.100 + b.10 + c = a.10 2 + b.10 1 + c
e﴿ abcde = a.10000 + b.1000 + c.100 + d.10 + e = a.10 4+ b.10 3+ c.10 2+ d.10 1 + e
\(213=\)\(2.10^2\) \(+1.10+3.10^0\)
\(421=4.10^2+2.10+1.10^0\)
\(1256=1.10^3+2.10^2+1.10^0\)
\(2006=2.10^3+0.10^2+0.10+6.10^0\)
abc = a . 10 ^2 + b .10 + c .10 ^ 0
abcde = a.10 ^ 4 + b.10^3 + c.10^ 2+ d .10 + e . 10 ^ 0
k cho mk nha
1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
213= 10 mũ 2+10 mũ 2+10 mũ 1 cộng 10 mũ 0 cộng 10 mũ 0 cộng 10 mũ 0
421=10 mũ 2+10 mũ 2+10 mũ 2+10 mũ 2 +10 mũ 1 + 10 mũ 1 +10 mũ 0
2009=10 mũ 3 + 10 mũ 3 + 10 mũ 0+10 mũ 0 + 10 mũ 0 +10 mũ 0 +10 mũ 0 +10 mũ 0 +10 mũ 0 +10 mũ 0+10 mũ 0 +10 mũ 0
abc= a.10 mũ 2+b.10 +c.10 mũ 0
abcde = 10 mũ 4.a +10 mũ 3.b +10 mũ 2.c +10.d +10 mũ 0.e
\(213=10^2+10^2+10^1+10^0+10^0+10^0\)
\(421=10^2+10^2+10^2+10^2+10^1+10^1+10^0\)
\(2009=10^3+10^3+10^0+10^0+10^0+10^0+10^0+10^0+10^0+10^0+10^0\)
\(abc=10^2\times a+10^1\times b+10^0\times c\)
\(abcde=10^4\times a+10^3\times b+10^2\times c+10^1\times d+10^0\times e\)
\(a,213=200+10+3\)\(=\left(2x10^2\right)\)\(+10^1\)\(+\left(3x10^0\right)\)
\(b,421=400+20+1\)\(=\left(4x10^2\right)\)\(+\left(2x10^1\right)\)\(+10^0\)
\(c,1256=1000+200+50+6\)\(=10^3\)\(+\left(2x10^2\right)\)\(+\left(5x10^1\right)\)\(+\left(6x10^0\right)\)
\(d,2006=2000+6\)\(=\left(2x10^3\right)\)\(+\left(6x10^0\right)\)
\(e,abc=100a+10b+c=10^2\)\(a+10^1\)\(b+\left(cx10^0\right)\)
\(g,abcde=10000a+1000b+100c+10d+e\)\(=10^4\)\(a+10^3\)\(b+10^2\)\(c+10^1\)\(d+e\)
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