a) \(\frac{10^4.81-16.15^2}{\left(-8\right)^4.3^{12}+6^{11}}=\frac{10^4.3^4-4^2.15^2}{8^4.3^{12}+6^{11}}=\frac{30^4-60^2}{2^{12}.3^{12}+6^{11}}=\frac{\left(30^2\right)^2-60^2}{6^{12}+6^{11}}\)

\(=\frac{900^2-60^2}{6^{11}.\left(6+1\right)}=\frac{60^2.\left(15^2-1\right)}{6^{11}.7}=\frac{60^2.224}{6^{11}.7}=\frac{2^9.3^2.5^2.7}{2^{11}.3^{11}.7}=\frac{5^2}{2^2.3^9}=\frac{25}{78732}\)

180 nha

Sai

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i) 58:252=58:(52)2=58:52.2=58:54=58−4=54

k) 49:642=49:(43)2=49:43.2=49:46=49−6=43

l) 225:324=225:(25)4=225:25.4=225:220=225−20=25

m) 1253:254=(53)3:(52)4=53.3:52.4=59:58=5

e) 38:36=38−6=32

f)  210:83=210:(23)3=210:23.3=210:29=210−9=2

g) 127:67=(12:6)7=27

h_ 215:813kết quả là số dư nên không tính ( đề sai )

a) 410.230=(22)10.230=22.10.230=220.230=220+30=250

b) 925.274.813=(32)25.(33)4.(34)3=33.25.33.4.34.3=375.312.312=375+12+12=399

c) 2550.1255=(52)50.(53)5=52.50.53.5=5100.515=5100+15=5115

d) 643.48.164=(43)3.48.(42)4=43.3.48.42.4=49.48.48=49+8+8=425

5⁷:5⁴=5^7-4=5³

10².10⁶=10²⁺⁶=10⁸

8³.8²=8³⁺²=8⁵

a) 2²⁷ = (2³)⁹ = 8⁹

3¹⁸ = (3²)⁹ = 9⁹

Do: 8 < 9 nên 8⁹ < 9⁹ hay 2²⁷ < 3¹⁸

b) 2⁹¹ = (2¹³)⁷ = 8192⁷

5³⁵ = (5⁵)⁷ = 3125⁷

Do: 8192 > 3125 nên 2⁹¹ > 5³⁵

c) 2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Do: 8 < 9 nên 2²²⁵ < 3¹⁵⁰

d) 9¹² = (3²)¹² = 3²⁴

27⁷ = (3³)⁷ = 3²¹

Do: 24 > 21 nên 9¹² > 27⁷

a) \(1^3+2^3+3^3+4^3 \)
\(=1+8+27+64\)
\(=100\)
\(=10^2\)

b)\(1^3+2^3+3^3+4^3+5^3\)
\(=1+8+27+64+125\)
\(=225\)
\(=15^2\)

Học dỏi nha :))
~ Good luck ~