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a,\(243^5=3^{5^5}=3^{5.5}=3^{25}\)
\(3.27^8=3.3^{3^8}=3.3^{3.8}=3.3^{24}=3^{25}\)
=>\(243^5=3.27^8\)
b,\(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)
\(81^3.125^5=3^{4^3}.5^{3^5}=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)
=>\(15^{12}< 81^3.125^5\)
c,\(78^{12}-78^{11}=78^{11}.\left(78-1\right)\)
\(78^{11}-78^{10}=78^{10}.\left(78-1\right)\)
=>\(78^{12}-78^{11}>78^{11}-78^{10}\)
Mình chỉ làm thế thôi lí luận và kết luận bạn tự làm nhé 
1: 243^5=(3^5)^5=3^25
3*27^8=3*3^24=3^25=243^5
3: 3^300=27^100
2^200=4^100
mà 27>4
nên 3^300>2^200
4: 15^2=3^2*5^2
81^3*125^3=3^12*5^9
=>15^2<81^3*125^3
6: 125^5=5^15
25^7=5^14
mà 15>14
nên 125^5>25^7
1: 243^5=(3^5)^5=3^25
3*27^8=3*(3^3)^8=3^25
=>243^5=3*27^8
6: 125^5=(5^3)^5=5^15
25^7=(5^2)^7=5^14
=>125^5>25^7(15>14)
5: 78^12-78^11=78^11(78-1)=78^11*77
78^11-78^10=78^10*77
mà 11>10
nên 78^12-78^11>78^11-78^10
a)\(1024^9=\left(2^{10}\right)^9=2^{90}< 2^{100}\)
b)\(27^{11}=\left(3^3\right)^{11}=3^{33}>3^{32}=\left(3^4\right)^8=81^8\)
c)\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
\(3^{30}=\left(3^3\right)^{10}=27^{10}\)
Ta có: \(25^{10}< 27^{10}\)
\(\Rightarrow5^{20}< 3^{30}\)
d) tương tự
e) \(78^{12}-78^{11}=78^{11}.\left(78-1\right)=78^{11}.77\)
\(78^{11}-78^{10}=78^{10}.\left(78-1\right)=78^{10}.77\)
Ta có: \(78^{11}.77>78^{10}.77\)
\(\Rightarrow78^{12}-78^{11}>78^{11}-78^{10}\)
f) \(333^{444}=\left[\left(111.3\right)^4\right]^{111}=\left(111^4.3^4\right)^{111}=\left(111^4.81\right)^{111}\)
\(444^{333}=\left[\left(111.4\right)^3\right]^{111}=\left(111^3.4^3\right)^{111}=\left(111^3.64\right)^{111}\)
Ta có: \(111^4.81>111^3.64\)
\(\Rightarrow\left(111^4.81\right)^{111}>\left(111^3.64\right)^{111}\)
\(\Rightarrow333^{444}>444^{333}\)
Tham khảo nhé~
a) Ta có :
\(1024^9=\left(2^{10}\right)^9=2^{90}\)
Vì \(2^{100}>2^{90}\)\(\Rightarrow\)\(2^{100}>1024^9\)
Vậy \(2^{100}>1024^9\)
b) Ta có :
\(27^{11}=\left(3^3\right)^{11}=3^{33}\)
\(81^8=\left(3^4\right)^8=3^{32}\)
Vì \(3^{33}>3^{32}\)\(\Rightarrow\)\(27^{11}>81^8\)
Vậy \(27^{11}>81^8\)
c) Ta có :
\(5^{20}=\left(5^2\right)^{10}=25^{10}\)
\(3^{30}=\left(3^3\right)^{10}=27^{10}\)
Vì \(25^{10}< 27^{10}\)\(\Rightarrow\)\(5^{20}< 3^{30}\)
Vậy \(5^{20}< 3^{30}\)
d) Ta có :
\(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
Vì \(8^{100}< 9^{100}\)\(\Rightarrow\)\(2^{300}< 3^{200}\)
Vậy \(2^{300}< 3^{200}\)
e) Ta có :
\(78^{12}-78^{11}=78^{11}.\left(78-1\right)=78^{11}.77\)
\(78^{11}-78^{10}=78^{10}\left(78-1\right)=78^{10}.77\)
Vì \(78^{11}>78^{10}\)\(\Rightarrow78^{11}.77>78^{10}.77\)
Hay \(78^{12}-78^{11}>78^{11}-78^{10}\)
Vậy \(78^{12}-78^{11}>78^{11}-78^{10}\)
f) Ta có :
\(333^{444}=\left(333^4\right)^{111}=\left[\left(3.111\right)^4\right]^{111}=\left(3^4.111^4\right)^{111}=\left(81.111^4\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}=\left[\left(4.111\right)^3\right]^{111}=\left(4^3.111^3\right)^{111}=\left(64.111^3\right)^{111}\)
Vì \(81.111^4>64.111^3\)\(\Rightarrow\)\(\left(81.111^4\right)^{111}>\left(64.111^3\right)^{111}\)
Hay \(333^{444}>444^{333}\)
Vậy \(333^{444}>444^{333}\)
_Chúc bạn học tốt_
a , >
b , ?????
c , >
Câu b là dấu < , bạn ak ^^!