a: \(5^{300}=25^{150}\)

\(3^{450}=27^{150}\)

mà 25<27

nên \(5^{300}< 3^{450}\)

a: 5300=251505300=25150

3450=271503450=27150

mà 25<27

nên 5300<3450

Ta có : \(A=1+2+2^2+...+2^{2017}\)(1)

\(\Rightarrow2A=2+2^2+2^3+...+2^{2018}\)(2)

Lấy (2) trừ (1) ta có : 

\(\Rightarrow A=2^{2018}-1\)

\(\Rightarrow A< B\). Vì \(B=2^{2018}\)

A = 1+2+2²+2³+.....+2²⁰¹⁷

2A = 2(1+2+2²+2³+.....+2²⁰¹⁷)  = 2+2²+2³+2⁴+.....+2²⁰¹⁸

2A - A = 2+2²+2³+2⁴+.....+2²⁰¹⁸- (1+2+2²+2³+.....+2²⁰¹⁷)

=> A = 2+2²+2³+2⁴+.....+2²⁰¹⁸-1-2-2²-2³-.....-2²⁰¹⁷

       A =2²⁰¹⁸-1 < 2²⁰¹⁸

Vậy A < B

\(a,4^{333}=\left(4^3\right)^{111}=64^{111}< 81^{111}=\left(3^4\right)^{111}=3^{444}< 3^{445}\\ b,39^{15}>36^{15}=\left(6^2\right)^{15}=6^{30}\\ c,25^{45}=\left(5^2\right)^{45}=5^{90}< 5^{102}=\left(5^3\right)^{34}=125^{34}\)

31¹¹<32¹¹=2⁵⁵

17¹⁴>16¹⁴=2⁵⁶

=>Vì 2⁵⁵<2⁵⁶ nên 31¹¹<17¹⁴.

a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)

b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)

c) \(27^{40}=3^{3^{40}}=3^{120}\)

\(64^{60}=8^{2^{60}}=8^{120}\)

Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)

con ai kooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

co don quaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

\(3^{2^{3^2}}=9^6\)

\(2^{3^{2^3}}=8^6\)

Vì \(9^6>8^6\)

\(\Rightarrow3^{2^{3^2}}>2^{3^{2^3}}\)

3^2^3^2<2^3^2^3

chắc zậy mà mink cũng ko chắc đâu nha!!!

các bạn ghi rõ lời giả và giải thích giùm mk nha !

2 mũ 6=(2 mũ 3)mũ2 =8 mũ 2 vậy 2 mũ 6 bằng 8 mũ2

8^2 = 2^3^2 = 2^(3x2) = 2^6

Vậy 2 số bằng nhau