Bài 1:

a, \(64^2=\left(2^6\right)^2=2^{12}\)

\(32^5=\left(2^5\right)^5=2^{25}\)

\(2^{12}< 2^{25}\Rightarrow64^2< 32^5\)

b, \(10^5=\left(5.2\right)^5=5^5.2^5\)

\(5^{10}=5^{5+5}=5^5.5^5\)

\(5^5.2^5< 5^5.5^5\Rightarrow10^5< 5^{10}\)

c, 256^ mấy thế hả bạn?

d, \(9^{200}=\left(9^2\right)^{100}=81^{100}\)

\(81^{100}>10^{100}\Rightarrow9^{200}>10^{100}\)

Bài 2:

\(9.27^2.81^3.216\)

\(=3^2.\left(3^3\right)^2.\left(3^4\right)^3.2^3.3^3\)

\(=3^2.3^6.3^{12}.3^3.2^3\)

\(=3^{2+6+12+3}.2^3\)

\(=3^{23}.2^3\)

nhung cach lam the nao ha ban , chi cho minh voi

may ban oi , cac cau lam sai rui , minh vua moi nhan ket qua la : 

a = 6 , n = 36

cam on cac ban da dong gop y kien , to cam on nhieu

a = 6

 n = 31

\(9^4.3^2\)

Cậu viết cái gì vậy

thì viết dưới dạng 1 lũy thừa mà

a: \(A=8^2\cdot32^4=2^6\cdot2^{20}=2^{26}\)

b: \(B=27^3\cdot9^4\cdot243=3^9\cdot3^8\cdot3^5=3^{22}\)

b) (2^3)^8=8^8

(3^2)^8=9^8

=>2^24<3^16(8^8<9^8)

1.a)

27⁵ và 243³ Ta có: 27⁵ = 14 348 907

                            243³ = 14 348 907

=> 27⁵ = 243³ ( vì 14 348 907 = 14 348 907 )

2^8 . 4^5 . 9^9

=2^8 . (2^2)^5 . (3^2)^9

=2^8 . 2^10 . 3^18

=2^18 . 3^18

=(3.2)^18

=6^18

\(2^8.4^5.9^9=2^8.\left(2^2\right)^5.\left(3^2\right)^9\)\(=2^8.2^{10}.3^{18}\)\(=2^{18}.3^{18}\)

\(2^8.4^5.9^9\)

\(=2^8.\left(2^2\right)^5.\left(3^2\right)^9\)

\(=2^8.2^{10}.3^{18}\)

\(=2^{18}.3^{18}\)

\(=\left(2.3\right)^{18}=6^{18}\)