viết về 1 lũy thừa
a) 4^10 . 8^15
b) 4^15. 5^30
c) 27^16.9^10
d) A = 72^3. 5^42 / 108^4
e) 3^10.11+3^10.5 / 3^9.2^4
K
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LH
1
22 tháng 8 2020
1. \(\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\frac{3^{10}\left(11+5\right)}{3^9\cdot2^4}=\frac{3^{10}\cdot2^4}{3^9\cdot2^4}=3\)
2. \(\frac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\frac{2^{10}\cdot\left(13+65\right)}{2^8\cdot104}=\frac{2^{10}\cdot78}{2^8\cdot104}=\frac{2^8\cdot2^2\cdot2\cdot3\cdot13}{2^8\cdot2^3\cdot13}=\frac{2^8\cdot2^3\cdot3\cdot13}{2^8\cdot2^3\cdot13}=3\)
3. \(\frac{72^2\cdot54^2}{108^4}=\frac{\left(2^3\cdot3^2\right)^2\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}\)
\(=\frac{2^6\cdot3^4\cdot2^2\cdot3^6}{2^8\cdot3^{12}}=\frac{2^8\cdot3^{10}}{2^8\cdot3^{12}}=\frac{3^{10}}{3^{12}}=3^{-2}=\frac{1}{9}\)
4. \(\frac{21^2\cdot14\cdot125}{35^5\cdot6}=\frac{\left(3\cdot7\right)^2\cdot2\cdot7\cdot5^3}{\left(5\cdot7\right)^5\cdot2\cdot3}=\frac{3^2\cdot7^2\cdot2\cdot7\cdot5^3}{5^5\cdot7^5\cdot2\cdot3}=\frac{3^2\cdot7^3\cdot2\cdot5^3}{5^3\cdot5^2\cdot7^2\cdot7^3\cdot2\cdot3}=\frac{3^2}{5^2\cdot3\cdot7^2}=\frac{3}{1225}\)
XO
1 tháng 8 2020
\(A=\frac{3^{10}.11+3^{10}.5}{3^9.2^4}=\frac{3^{10}.16}{3^9.16}=3\)
\(B=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.78}{2^8.104}=\frac{2^{10}.26.3}{2^8.2^2.26}=3\)
\(C=\frac{72^3.52^4}{108^4}=\frac{\left(3^2.2^3\right)^3.\left(13.2^2\right)^4}{\left(3^3.2^2\right)^4}=\frac{3^6.2^9.13^4.2^8}{3^{12}.2^8}=\frac{2^9.13^4}{3^6}\)
\(D=\frac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}=\frac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}=\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}\left(33-1\right)}{2^2.3^{28}}=\frac{3^{29}.2^5}{2^2.3^{28}}=3.8=24\)
K
9 tháng 10 2018
\(\frac{3^{10}.11+3^{10}.10}{3^9.2^4}\)
\(=\frac{3^{10}.\left(11+10\right)}{3^9.2^4}=\frac{3^{10}.21}{3^9.16}\)
\(=\frac{3.21}{16}=\frac{63}{16}\)
NV
1
NC
9 tháng 12 2019
3^10.11 + 3^10.5 : ( 3^9.2^4)
=3^10.(11+5) : (3^9.2^4)
=(3^10.16) : (3^9.16)
=3^10 : 3^9
=3
Có gì sai thì góp ý cho mình nhé, Tks ! :)))
MN
2
7 tháng 2 2022
A) 410 . 815 = (22)10 . (23)15 = 220 . 245 = 220+45=265
B) 415 . 530 = (22)15 . 530 = 230 . 530 = (2 . 5)30 = 1030
C) 2716 : 910 = (33)16 : (32)10 = 348 : 320 = 348-20=328
LM
Lê Minh Vũ
VIP
23 tháng 6 2023
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) \(a^7\div a^2=a^{7-2}=a^5\)
LM
Lê Minh Vũ
VIP
23 tháng 6 2023
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
N
4 tháng 8 2019
a) 53.252:54
= 53.(52)2:54
= 53.54:54
= 53+4-4
= 53
b) 42.(23)2:128
= (22)2.26:27
= 24.26:27
= 24+6-7
= 23
c) 35.243:(32)3
= 35.35:36
= 35+5-6
= 34
d) 205:55
= (20:5)5
= 45
e) 410:810 (Có chắc không vậy ? Hay là 810:410 ?)
g) 415.530
= 415.(52)15
= 415.2515
= (4.25)15
= 10015
h) 2716.910
= (33)16.(32)10
= 348.320
= 348+20
= 368
\(a,4^{10}\cdot8^{15}=2^{20}\cdot2^{45}=2^{65}\)
\(b,4^{15}\cdot5^{30}=4^{15}\cdot5^{15}\cdot5^{15}=\left(4\cdot5\cdot5\right)^{15}=100^{15}\)
\(c,27^{16}\cdot9^{10}=3^{48}\cdot3^{20}=3^{68}\)
a) \(4^{10}.8^{15}=\left(2^2\right)^{10}.\left(2^3\right)^{15}=2^{20}.2^{45}=2^{20+45}=2^{65}\)
b) \(4^{15}.5^{30}=\left(2^2\right)^{15}.5^{30}=2^{30}.5^{30}=\left(2.5\right)^{30}=10^{30}\)
c) \(27^{16}.9^{10}=\left(3^3\right)^{16}.\left(3^2\right)^{10}=3^{48}.3^{20}=3^{48+20}=3^{68}\)