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a,�,
220.15+210.85220.15+210.85
=220.210.85+15=220.210.85+15
=230.100=230.100
=230.102=230.102
b,�,
2716:9102716:910
=(33)16:(32)10=(33)16:(32)10
=348:320=348:320
=328=328
c,�,
1253:2541253:254
=(53)5:(52)4=(53)5:(52)4
=515:58=515:58
=57=57
d,�,
244:34−3212:1612244:34−3212:1612
=(24:3)4−(32:16)12=(24:3)4−(32:16)12
=84−212=84−212
=(23)4−212=(23)4−212
=212−212=212−212
a. \(5^{10}.125^2.625^3=5^{10}.\left(5^3\right)^2.\left(5^4\right)^3=5^{10}.5^6.5^{12}=5^{10+6+12}=5^{28}\)
a: \(=5^{10}\cdot5^6\cdot5^{12}=5^{28}\)
b: \(=10^3\cdot10^8\cdot10^{15}=10^{26}\)
c: \(=2^{20}\cdot2^{20}=2^{40}\)
d: \(=2^{16}\cdot2^{16}\cdot3^8=2^{32}\cdot3^8\)
e: \(=\dfrac{3^{24}}{3^8}=3^{16}\)
f: \(=2^{12}\cdot2^{20}\cdot2^5=2^{37}\)
\(16^4:4^2\)
\(=\left(4^2\right)^4:4^2\)
\(=4^8:4^2=4^6\)
b) \(27^8:9^4\)
\(=\left(3^3\right)^8:\left(3^2\right)^4\)
\(=3^{24}:3^8=3^{16}\)
Cậu còn lại bạn làm tương tư nha
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link đó
\(16^6:4^2=2^{24}:2^4=2^{24-4}=2^{20}\)
\(12^n:2^{2n}=12^n:4^n=3^n\)
\(27^8:9^4=3^{24}:3^8=3^{24-8}=3^{16}\)
\(125^5:25^3=5^{15}:5^6=5^{15-6}=5^9\)
\(4^{14}.5^{28}=4^{14}.25^{14}=\left(4.25\right)^{14}=100^{14}\)
\(64^4.16^5:4^{20}=2^{24}.2^{20}:2^{40}=2^{24+20-40}=2^4=16\)
Bài 4: Viết các tích sau đây dưới dạng 1 lũy thừa của 1 số
A = 82.324 = ( 23 )2 . ( 25 )4 = 26 . 220 = 226
B = 273.94.243 = ( 33 )3 . ( 32 )4 . 35 = 39 . 38 . 35 = 322
C = 410.815 = ( 22 )10 . ( 23 )15 = 220 . 245 = 265
D = 415.530 = ( 22 )15 . 530 = 230 . 530 = ( 2 . 5 )30 = 1030
E = 2716 : 910 = ( 33 )16 . ( 32 )10 = 348 . 320 = 368
F = 25.84 = 25 . ( 23)4 = 25 . 212= 217
g = 256.1253 = ( 52 )6 . ( 53 )3 = 512 . 59 = 521
H = 123.33 = ( 12.3 )3 = 363
\(4^8.2^{20}.9^{12}.27^5.81^4.25^{20}.125^4\)
\(=\left(2^2\right)^8.2^{20}.\left(3^2\right)^{12}.\left(3^3\right)^5.\left(3^4\right)^4.\left(5^2\right)^{20}.\left(5^3\right)^4\)
\(=2^{16}.2^{20}.3^{15}.3^{16}.5^{40}.5^{12}\)
\(=2^{16+20}.3^{15+16}.5^{40+12}\)
\(=2^{36}.3^{31}.5^{52}\)
Nữ hoàng cảm ơn nhưng vị thám tử tài ba có thể viết cách giải ra đc không ạ
\(a,81^3\cdot\frac{1}{9^2}:3^3=\left(9^2\right)^3\cdot\frac{1}{9^2}:3^3=9^6\cdot\frac{1}{9^2}\cdot\frac{1}{3^3}=\frac{9^6}{9^2}\cdot\frac{1}{3^3}=9^4\cdot\frac{1}{3^3}=\left(3^2\right)^4\cdot\frac{1}{3^3}=\frac{3^8}{3^3}=3^5\)
\(b,625^4:25^2=\left(5^4\right)^4:\left(5^2\right)^2=5^{16}:5^4=5^{12}\)
Bạn ấy lm câu a rùi mik lm 3 câu còn lại nha
\(27^{16}:9^{10}\)
\(=3^{16}\cdot9^{16}:9^{10}\)
\(=9^8\cdot9^6=9^{14}\)
\(125^3:25^4\)
\(=5^3\cdot25^3:25^4\)
\(=5\cdot25\cdot25^3:25^4\)
\(=5\cdot25^4:25^4\)
\(=5\cdot1=5\)
\(24^4:3^4-32^{12}:16^{12}\)
\(=8^4\cdot3^4:3^4-2^{12}\cdot16^{12}:16^{12}\)
\(=8^4-2^{12}\)
\(=4096-4096\)
\(=0\)
\(2^{20}\)\(.15+20^{10}.85\)
=15728640+8,704x1014
=8,704000157x1014