(-1/5)^300= [(-1/5)^3]^100=(1/125)^100

(-1/3)^500=[(-1/3)^5]^100=(1/243)^100 

k mik tròn 45 nhé

Ta có: \(\left(\frac{1}{3}\right)^{300}

Ta có :

\(-\left(\frac{1}{3}\right)^{500}=-\left(\frac{1}{3}\right)^{5.100}=\) \(-\left(\frac{1}{243}\right)^{100}\)

\(-\left(\frac{1}{5}\right)^{300}=-\left(\frac{1}{5}\right)^{3.100}\) =\(-\left(\frac{1}{125}\right)^{100}\) 

Vì  \(-\left(\frac{1}{125}\right)< -\left(\frac{1}{243}\right)\)nên \(-\left(\frac{1}{3}\right)^{500}>-\left(\frac{1}{5}\right)^{300}\)

(-1/3)^500 >(-1/3)^300 . Vì 500 > 300 (so sánh 2 lũy thừa cùng cơ số , số nào có số mũ lớn hơn thì số đó lớn hơn và ngược lại)

Ta có :

\(\left(\frac{-1}{3}\right)^{500}=\left(\frac{1}{3}\right)^{500}\)

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

Vì 500 > 300

=> \(\left(\frac{1}{3}\right)^{500}< \left(\frac{1}{3}\right)^{300}\)

=> \(\left(\frac{-1}{3}\right)^{500}< \left(\frac{-1}{3}\right)^{300}\)

ta có  (-1/3)⁵⁰⁰=[(-1/3)^5]100=(-1/243)¹⁰⁰   

(-1/3)³⁰⁰=[(-1/3)^3]100=(-1/27)¹⁰⁰

Vì (-1/243)¹⁰⁰>(-1/27)¹⁰⁰=>(-1/3)⁵⁰⁰>(-1/3)³⁰⁰

Ta có :

 \(\frac{1^{500}}{2}=\frac{1}{2}\)

\(\frac{1^{300}}{3}=\frac{1}{3}\)

Mà 3>2

\(\Rightarrow\frac{1}{2}>\frac{1}{3}\)

Hay \(\frac{1^{500}}{2}>\frac{1^{300}}{3}\)

\(\left(\frac{1}{3}\right)^{500}=\left(\frac{1}{3}^5\right)^{100}=\frac{1}{243}^{100}\)

\(\left(\frac{1}{5}\right)^{300}=\left(\frac{1}{5}^3\right)^{100}=\frac{1}{125}^{100}\)

Vì \(\frac{1}{243}<\frac{1}{125}=>\frac{1}{243}^{100}<\frac{1}{125}^{100}=>\left(\frac{1}{3}\right)^{500}<\left(\frac{1}{5}\right)^{300}\)

3^-500=(3⁵)^-100= 243^-100

5^-300= (5³)^-100 =125^-100

^{243>125 =>}    243^-100<125^-100

Hay 3^-500 <5^-300

\(\left(-\frac{1}{5}\right)^{300}=-\frac{1^{300}}{5^{300}}=-\frac{1}{5^{300}}\)

\(\left(-\frac{1}{5}\right)^{500}=-\frac{1^{500}}{5^{500}}=-\frac{1}{5^{500}}\)

Ta có : 

\(5^{300}< 5^{500}\)

\(\Rightarrow-5^{300}>-5^{500}\)

\(\Rightarrow-\frac{1}{5^{300}}>-\frac{1}{5^{500}}\)

\(\Rightarrow\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{5}\right)^{500}\)

Ta co : 3⁵⁰⁰ va -5³⁰⁰

=>3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰                        (1)

=>-5³⁰⁰=(-5³)¹⁰⁰=-125¹⁰⁰                            (2)
Tu (1) va (2) suy ra 3500>-5300

lik e nhe

3⁵⁰⁰ và -5³⁰⁰

3⁵⁰⁰  = ( 3 ⁵ ) ¹⁰⁰ = 243¹⁰⁰

 -5³⁰⁰ = ( -5 ³)¹⁰⁰ = -125¹⁰⁰

do 243  > -125 nên => 243¹⁰⁰ >  -125¹⁰⁰

=> 3⁵⁰⁰  > -5³⁰⁰ 

^{tick nhé}

Ta có:

(-1/5)³⁰⁰ = (-1)³⁰⁰/5³⁰⁰ = 1/(5³)¹⁰⁰ = 1/125¹⁰⁰

(-1/3)⁵⁰⁰ = (-1)⁵⁰⁰/3⁵⁰⁰ = 1/(3⁵)¹⁰⁰ = 1/243¹⁰⁰

Vì 125¹⁰⁰ < 243¹⁰⁰

=> 1/125¹⁰⁰ > 1/243¹⁰⁰

=> (-1/5)³⁰⁰ > (-1/3)⁵⁰⁰

Ta có : \(\left(-\frac{1}{5}\right)^{300}=\left(-\frac{1}{5}\right)^{3.100}=\left(-\frac{1}{125}\right)^{100}=\left(\frac{1}{125}\right)^{100}\)

            \(\left(-\frac{1}{3}\right)^{500}=\left(-\frac{1}{3}\right)^{5.100}=\left(-\frac{1}{243}\right)^{100}=\left(\frac{1}{243}\right)^{100}\)

Mà \(125< 243\Rightarrow\frac{1}{125}>\frac{1}{243}\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{243}\right)^{100}\)

\(=>\left(-\frac{1}{5}\right)^{300}>\left(-\frac{1}{3}\right)^{500}\)

Ta có:

(-1/5)³⁰⁰ = (-1)³⁰⁰/5³⁰⁰ = 1/(5³)¹⁰⁰ = 1/125¹⁰⁰

(-1/3)⁵⁰⁰ = (-1)⁵⁰⁰/3⁵⁰⁰ = 1/(3⁵)¹⁰⁰ = 1/243¹⁰⁰

Vì 125¹⁰⁰ < 243¹⁰⁰

=> 1/125¹⁰⁰ > 1/243¹⁰⁰

=> (-1/5)³⁰⁰ > (-1/3)⁵⁰⁰