Ta có :

3⁵⁴ = ( 3² )²⁷ = 9²⁷

2⁸¹ = ( 2³ )²⁷ = 8²⁷

Vì 9²⁷ > 8²⁷ nên 3⁵⁴ > 2⁸¹

2 mũ 81nha

3\(^{54}\)>    2\(^{81}\)

\(10^{30}vs\)\(2^{100}\)

\(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì \(1000^{10}< 1024^{10}=>10^{30}< 2^{100}\)

\(3^{54}vs2^{81}\)

\(3^{54}=\left(3^6\right)^9=729^9\)

\(2^{81}=\left(2^9\right)^9=512^9\)

Vì \(729^9>512^9=>3^{54}>2^{81}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

\(2^{300}=\left(2^3\right)^{100}=8^{100}\)

Vì \(8^{100}< 9^{100}=>2^{300}< 3^{200}\)

Bài 1: a)  \(M=1+5+5^2+...+5^{100}\)

\(5M=5+5^2+5^3+...+5^{101}\)

\(5M-M=\left(5+5^2+5^3+...+5^{101}\right)-\left(1+5+5^2+...+5^{100}\right)\)

\(4M=5^{101}-1\)

\(M=\frac{5^{101}-1}{4}\)

b) \(N=2+2^2+...+2^{100}\)

\(2N=2^2+2^3+...+2^{101}\)

\(2N-N=\left(2^2+2^3+...+2^{101}\right)-\left(2+2^2+...+2^{100}\right)\)

\(N=2^{101}-2\)

Bài 2:

a) \(16^{32}=\left(2^4\right)^{32}=2^{128}\) 

\(32^{16}=\left(2^5\right)^{16}=2^{80}\)

Vì \(2^{128}>2^{80}\Rightarrow16^{32}>32^{16}\)

MÌNH KHÔNG HIỂU GÌ CẢ

ta thấy: 5^300=5^3.100=(5^3)^100=125^100

            3^453=3^5.143=(3^5)^143=125^143

    Vì 100<143=>125^100<125^143

hay 5^300<3^453

vậy 5^300<3^453

Đề sai rồi

sao tính được

5^300 va 5^400 con giai dc . sai de rui bn

\(2\cdot2^{15}=2^{16}=2^3\cdot2^{13}=8\cdot2^{13}>7\cdot2^{13}\)

Vậy \(7\cdot2^{13}< 2\cdot2^{15}\)

.

7.2 mũ > 2.2 mũ 15

ta có:2.2^15=2^16=2^13.2^3=2^13.8

vì 2^13.8 > 2^13.7 nên 2.2^15 > 7.2^13

A=1+2+2²+2³+...+2^{2017 (1)}

2A=2+2²+2³+2⁴+...+2^{2018 (2)}

Lấy (2) - (1) ta có:

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

Mà B=2²⁰¹⁸-1 =>A=B

b) ta có: B=2017²

B=(2016+1).2017=2016.2017+2017

A=2016.2018

A=2016.(2017+1)=2016.2017+2016

Vì 2016<2017=>A<B

mình nhé

a, A = 1+2+2²+...+2²⁰¹⁷

2A=2+2²+2³+...+2²⁰¹⁸

2A-A=A=2²⁰¹⁸-1

=> A  = B

b, A = 2016.2018 =2016.(2017+1)=2016+2017.2016

B=2017²=2017.2017=2017.(2016+1)=2017.2016+2017

Vì 2016 < 2017 => 2016+2017.2016 < 2017.2016+2017 => A < B

cảm ơn nhé, Hoàng

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

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