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

i do not care about you

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,\(243^5=3^{5^5}=3^{5.5}=3^{25}\)

\(3.27^8=3.3^{3^8}=3.3^{3.8}=3.3^{24}=3^{25}\)

=>\(243^5=3.27^8\)

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

a,243⁵=(3⁵)⁵=3²⁵

3.27⁸=3.(3³)⁸=3.3²⁴=3²⁵

Vì 3²⁵=3²⁵ nên 243⁵=3.27⁸

b,81³.125⁵=(3⁴)³.(5³)⁵

=3¹².5¹⁵

=15¹².5³

=>15¹²<81³.125⁵

c,78¹²-78¹¹=78¹¹(78-1)=77.78¹¹

78¹¹-78¹⁰=78¹⁰(78-1)=77.78¹⁰

Vì 77.78¹⁰<77.78¹¹=>78¹²-78¹¹>78^1`1-78¹⁰

help me

a , >

b , ?????

c , >

Câu b là dấu < , bạn ak ^^!

c, 78 ¹² - 78¹¹ và 78¹¹ - 78¹⁰

Ta có : 78¹² - 78¹¹ = 78¹¹ . 78 - 78¹¹ . 1

                                  =78¹¹ . (78-1) = 78¹¹ . 77

             78¹¹ - 78¹⁰ = 78¹⁰ . 78 - 78¹⁰ .1

                                  = 78¹⁰ . (78-1) = 78¹⁰ . 77

+/ Vì 78¹⁰ lớn hơn 78¹¹ nên 78¹¹ . 77 lớn hơn 78¹⁰ . 77

    Vậy 78¹² - 78¹¹ lớn hơn 78¹¹ - 78¹⁰.

\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)

\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)

\(4^{21}=\left(4^3\right)^7=64^7>64^2\)

\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)

\(31^{11}16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)

Các bài khác làm tương tự

a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)

Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)

b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)

\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)

Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)