33⁵²<44³⁹

\(a,\) Ta có : \(\hept{\begin{cases}2^{10}=2^{10}\\3^{12}=3^{10}.3^2\end{cases}}\)

Vì \(3^{10}>2^{10}\Rightarrow2^{10}< 3^{10}.3^2\)

Hay \(2^{10}< 3^{12}\)

\(b,\)  Ta có : \(\hept{\begin{cases}33^{52}=\left(33^4\right)^{13}=1185921^{13}\\44^{39}=\left(44^3\right)^{13}=85184^{13}\end{cases}}\)

Vì \(1185921^{13}>85184^{13}\)

Do đó : \(33^{52}>44^{39}\)

\(33^{52}=3^{52}.11^{52}=81^{13}.\left(11^4\right)13\)

\(44^{39}=4^{39}.11^{39}=64^{13}.\left(11^3\right)^{13}\)

Ta có\(11^4>11^3\)\(\Rightarrow11^{52}>11^{39}\)(1)

\(81^{13}>64^{13}\Rightarrow3^{52}>4^{39}\)(2)

Từ (1) và (2)\(\Rightarrow33^{52}>44^{39}\)

mk nghĩ là  \(33^{52}\)>\(44^{39}\)ngắn gọn nhất

lập luận j z 

\(3^{-200}=\left(3^{-2}\right)^{100}=\left(\frac{1}{9}\right)^{100}\)

\(2^{-300}=\left(2^{-3}\right)^{100}=\left(\frac{1}{8}\right)^{100}\)

\(\frac{1}{9}< \frac{1}{8}\Rightarrow\left(\frac{1}{9}\right)^{100}< \left(\frac{1}{8}\right)^{100}\Rightarrow3^{-200}< 2^{-300}\)

\(33^{52}=\left(33^4\right)^{13}\)

\(44^{39}=\left(44^3\right)^{13}\)

\(33^4=\left(33^{\frac{4}{3}}\right)^3\approx106^3\)

\(106^3>44^3\Rightarrow\left(33^4\right)^{13}> \left(44^3\right)^{13}\Rightarrow33^{52}>44^{39}\)

giải 

a)3^-200<2^-300

b)33^52>44^39

3^-200=3^(-2x100) 

2^-300=2^(-3x100)

=2^-300>3^-200

chúc bn học tốt

a, 3^(−200) và 2^(−300)

Ta có :

3^(−200) =(3^−2)^100=(1/9)^100

2^(−300) =(2^−3)^100=(1/8)^100

Do 1/9<1/8 nên 3^(−200) < 2^(−300)

b, 33^52 và 44^39 

Ta có :

33^52 = ( 33^4)^13

44^39 = ( 44^3 )^13

33^4 = ( 33 4/3 )^3 = 106^3

106^3 > 44^3 ⇒ ( 33^4)^13 > ( 44^3 )^13 ⇒ 33^52 >44^39

#Học tốt#

a, ta có:

\(3^{\left(-200\right)}=\left(3^{-2}\right)^{100}=\left(\frac{1}{9}\right)^{100}\)

\(2^{\left(-300\right)}=\left(2^{-3}\right)^{100}=\left(\frac{1}{8}\right)^{100}\)

Vì \(\frac{1}{9}< \frac{1}{8}\Rightarrow\left(\frac{1}{9}\right)^{100}< \left(\frac{1}{8}\right)^{100}\Rightarrow3^{\left(-200\right)}< 2^{\left(-300\right)}\)

Có 44³⁹=44^3.13=(44³)¹³=85184¹³

33⁵²= 33^4.13=(33⁴)¹³=1185921¹³

mà 85184¹³ < 1185921¹³

<=> 44³⁹<33⁵²

\(33^{44}=33^{4.11}=\left(33^4\right)^{11}=1185921^{11}\)

\(44^{33}=44^{3.11}=\left(44^3\right)^{11}=85184^{11}\)

Vì \(1185921^{11}>85184^{11}\)

Nên \(33^{44}>44^{33}\)

tích nnha !!!

3344   <   4433

mình nghĩ là 33^44>44^33