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\(14^4.4^2.21^5.28^3.18^3\)
\(=\left(7.2\right)^{14}.\left(2^2\right)^2.\left(7.3\right)^5.\left(7.2^2\right)^3.\left(3^2.2\right)^3\)
\(=7^{14}.2^{14}.2^4.7^5.3^5.7^3.2^6.3^6.2^3\)
\(=\left(7^{14}.7^5.7^3\right)\left(2^{14}.2^4.2^6.2^3\right)\left(3^5.3^6\right)\)
\(=7^{22}.2^{27}.3^{11}\)
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) $10^6:10=10^{6-1}=10^5$
$5^8:25^2=5^8:(5^2)^2=5^8:5^4=5^{8-4}=5^4$
$4^9:64^2=4^9:(4^3)^2=4^9:4^6=4^{9-6}=4^3$
$2^25:32^4=2^{25}:(2^5)^4=2^{25}:2^{20}=2^{25-20}=2^5$
$18^3:9^3=(18:9)^3=2^3$
\(\cdot3^8:3^6=3^{8-6}=3^2\)
\(\cdot19^7:19^3=19^{7-3}=19^4\)
\(\cdot2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^9=2\)
\(\cdot12^7:6^7=\left(12:6\right)^7=2^7\)
\(\cdot27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3\)
\(\cdot10^6:10=10^{6-1}=10^5\)
\(\cdot5^8:25^2=5^8:\left(5^2\right)^2=5^8:5^4=5^4\)
\(\cdot4^9:64^2=4^9:\left(4^3\right)^2=4^9:4^6=4^3\)
\(2^{25}:32^4=2^{25}:\left(2^5\right)^4=2^{25}:2^{20}=2^5\)
\(18^3:9^3=\left(18:9\right)^3=2^3\)
a) $125^3:25^4=(5^3)^3:(5^2)^4=5^9:5^8=5^1$
$16^4:4^2=(4^2)^4:4^2=4^8:4^2=4^6$
$27^8:9^4=(3^3)^8:(3^2)^4=3^{24}:3^8=3^{16}$
$125^5:25^3=(5^3)^5:(5^2)^3=5^{15}:5^6=5^9$
$4^{14}:5^{28}=(2^2)^{14}:5^{28}=2^{28}:5^{28}=(\dfrac{2}{5})^{28}$
b) $12^n:2^{2n}=12^n:(2^2)^n=12^n:4^n=3^n$
$64^4.16^5.4^{20}=(4^3)^4.(4^2)^5.4^{20}=4^{12}.4^{10}.4^{20}=4^{42}$
\(a,213=200+10+3\)\(=\left(2x10^2\right)\)\(+10^1\)\(+\left(3x10^0\right)\)
\(b,421=400+20+1\)\(=\left(4x10^2\right)\)\(+\left(2x10^1\right)\)\(+10^0\)
\(c,1256=1000+200+50+6\)\(=10^3\)\(+\left(2x10^2\right)\)\(+\left(5x10^1\right)\)\(+\left(6x10^0\right)\)
\(d,2006=2000+6\)\(=\left(2x10^3\right)\)\(+\left(6x10^0\right)\)
\(e,abc=100a+10b+c=10^2\)\(a+10^1\)\(b+\left(cx10^0\right)\)
\(g,abcde=10000a+1000b+100c+10d+e\)\(=10^4\)\(a+10^3\)\(b+10^2\)\(c+10^1\)\(d+e\)
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
Bài 1 :
a/ \(a^3.a^9=a^{3+9}=a^{12}\)
b/\(\left(a^5\right)^7=a^{5.7}=a^{35}\)
c/ \(\left(a^6\right).4.a^{12}=a^{24}.a^{12}.4=a^{24+12}.4=a^{36}.4\)
d/ \(\left(2^3\right)^5.\left(2^3\right)^3=2^{15}.2^9=2^{15+9}=2^{24}\)
e/ \(5^6:5^3+3^3.3^2\)
\(=5^3+3^5=125+243=368\)
i/ \(4.5^2-2.3^2\)
\(=2^2.5^2-2.3^2\)
\(=2^2.25-2^2.14\)
\(=2^2.\left(25-14\right)\)
\(=2^2.11\)
\(=4.11=44\)
a) \(4^{10}.2^{30}=\left(2^2\right)^{10}.2^{30}=2^{2.10}.2^{30}=2^{20}.2^{30}=2^{20+30}=2^{50}\)
b) \(9^{25}.27^4.81^3=\left(3^2\right)^{25}.\left(3^3\right)^4.\left(3^4\right)^3=3^{3.25}.3^{3.4}.3^{4.3}=3^{75}.3^{12}.3^{12}=3^{75+12+12}=3^{99}\)
c) \(25^{50}.125^5=\left(5^2\right)^{50}.\left(5^3\right)^5=5^{2.50}.5^{3.5}=5^{100}.5^{15}=5^{100+15}=5^{115}\)
d) \(64^3.4^8.16^4=\left(4^3\right)^3.4^8.\left(4^2\right)^4=4^{3.3}.4^8.4^{2.4}=4^9.4^8.4^8=4^{9+8+8}=4^{25}\)
e) \(3^8:3^6=3^{8-6}=3^2\)
f) \(2^{10}:8^3=2^{10}:\left(2^3\right)^3=2^{10}:2^{3.3}=2^{10}:2^9=2^{10-9}=2\)
g) \(12^7:6^7=\left(12:6\right)^7=2^7\)
h_ \(21^5:81^3\)kết quả là số dư nên không tính ( đề sai )
a) = 53+4+1 = 58
b) = 65-4 = 6
c) = 32+3+4-7 = 32
d) = x4+2+1 = x7
e) = 812+10+3 = 825
1. \(5^3.5^4.5=5^{3+4+1}=5^8\)
2. \(6^5:\left(6^3.6\right)=6^5:\left(6^{3+1}\right)=6^5:6^4=6^{5-4}=6^1\)
3. \(\left(3^2.3^3.3^4\right):3^7=\left(3^{2+3+4}\right):3^7=3^9:3^7=3^{9-7}=3^2\)
4. \(x^4.x^2.x=x^{4+2+1}=x^7\)
5. \(\left(8^{12}.8^{10}\right).8^3=8^{12+10+3}=8^{25}\)
144.492.215.283.183
=(2.7)4.(72)2.(3.7)5.(22.7)3.(32.2)3
=24.74.74.35.75.26.73.36.23
=213.311.721
405.105.86.207
=(5.23)5.(2.5)5.(23)6.(5.22)7
=55.215.25.55.218.57.214
=252.517
304.124.252.187
=(2.3.5)4.(22.3)4.(52)2.(2.32)7
=24.34.54.28.34.54.27.314
=219.322.58