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a, 25 . 84 = 25 . (23)4 = 25 . 212 = 25+12 = 217
b, 256 . 1253 = (52)6 . (53)3 = 512 . 59 = 512+9 = 521
c, 6255 : 257 = (54)5 : (52)7 = 520 : 514 = 520-14 = 56
d, 123 . 33 = ( 3 . 22 )3 . 33 = 33 .26 . 33 = 33+3 . 26 = 36 . 26 = (3.2)6 = 66
\(125=5^3\)
\(25^2=\left(5^2\right)^2=5^{2.2}=5^4\)
\(\left(5^3\right)^2=5^{3.2}=5^6\)
\(125^5=\left(5^3\right)^5=5^{3.5}=5^{15}\)
\(625^4=\left(5^4\right)^4=5^{4.4}=5^{16}\)
\(125.5^2=5^3.5^2=5^{3+2}=5^5\)
125 = 53
252 = (52)2 = 54
(53)2 = 56
1255 = ( 53)5 = 515
6254 = (54)4 = 516
125 . 52 = 53 . 52 = 55
a) \(\left(20.2^4+12.2^4-48.2^2\right):8^2\)
\(=\left(20.2^4+12.2^4-12.2^4\right):8^2\)
\(=2^4.\left(20+12-12\right):8^2\)
\(=16.20:64\)
\(=5\)
=54 . (75+175) ÷ 15625
=54 . .250 ÷ 56
=(54 ÷56) . 250
=0,04 . 250
=10
a) \(25^6\cdot125^3=\left(5^2\right)^6\cdot\left(5^3\right)^3=5^{12}\cdot5^9=5^{21}\)
b) \(625^5:25^7=\left(5^4\right)^5:\left(5^2\right)^7=5^{20}:5^{14}=5^6\)
c) \(12^3\cdot3^3=\left(12\cdot3\right)^3=36^3\)
1, \(81\cdot27^3\cdot243^5=3^4\cdot3^9\cdot3^{25}=3^{38}\)
2,\(25^4\cdot125^3\cdot625^7=5^8\cdot5^9\cdot5^{28}=5^{45}\)
3,
\(16^3\cdot8^9\cdot64^5\cdot1024=2^{12}\cdot2^{27}\cdot2^{30}\cdot2^{10}=2^{79}\)
\(2^5.4=2^5.2^2=2^7\);\(5^4.25=5^4.5^2=5^6\); \(16^3.2^3=\left(2^4\right)^3.2^3=2^{12}.2^3=2^{15}\)
\(625^5:25^7=\left(5^4\right)^5:\left(5^2\right)^7=5^{20}:5^{14}=5^6\); \(25^6:125^3=\left(5^2\right)^6:\left(5^3\right)^3=5^{12}:5^9=5^3\)
\(12^4.3^4=\left(2^2.3\right)^4.3^4=2^8.3^4.3^4=2^8.3^8=6^8\); \(9^6:3^2=\left(3^2\right)^6:3^2=3^{12}:3^2=3^{10}\)
\(2^3.2^4.2=2^8\)
câu hỏi???
`5^12 .25^4 .125^3 .625^2=5^12 . (5^2)^4 . (5^3)^3 . (5^4)^2 =5^12 .5^8 .5^9 .5^8=5^37`