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

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

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

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

a,>

b,=

c,>

Chắc đấy! Tick nhé!

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

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

Mà \(\frac{1}{125^{100}}>\frac{1}{243^{100}}\)

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

b)Ta có :\(2^{90}=\left(2^{15}\right)^6=32768^6\)

\(5^{36}=\left(5^6\right)^6=15625^6\)

Vì \(32768^6>15625^6\Rightarrow2^{90}>5^{36}\)

a.Ta có: \(\left(\frac{-1}{5}\right)^{300}=\left(\frac{-1}{5}^3\right)^{100}=\left(\frac{-1}{125}\right)^{100}=\left(\frac{1}{125}\right)^{100}\)

\(\left(\frac{-1}{3}\right)^{500}=\left(\frac{-1}{3}^5\right)^{100}=\left(\frac{-1}{243}\right)^{100}=\left(\frac{1}{234}\right)^{100}\)

Mà: \(\frac{1}{125}>\frac{1}{234}\Rightarrow\left(\frac{1}{125}\right)^{100}>\left(\frac{1}{234}\right)^{100}\)

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

b.Ta có: \(2^{90}=\left(2^{10}\right)^9=1024^9\)

\(5^{36}=\left(5^4\right)^9=625^9\)

Mặt khác: \(1024>625\Rightarrow1024^9>625^9\)

 Vậy \(2^{90}>5^{36}\)

Ta có : (-1/5)^300=(-1/5^3)100=(-1/125)^100

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

vì (-1/243)^100<(-1/125)^100→(-1/5)^300>(-1/3)^500

b, ta có:-(-2)^300=(2^3)^100=8^100

(-3)^200=(-3^2)^100=9^100

vì 8^100<9^100→-(-2)^300<(-3)^200

a) \(\frac{3}{4} + \left( {\frac{1}{2} - \frac{1}{3}} \right) = \frac{9}{{12}} + \left( {\frac{6}{{12}} - \frac{4}{{12}}} \right) = \frac{9}{{12}} + \frac{2}{{12}} = \frac{{11}}{{12}}\)

\(\frac{3}{4} + \frac{1}{2} - \frac{1}{3} = \frac{9}{{12}} + \frac{6}{{12}} - \frac{4}{{12}} = \frac{{15}}{{12}} - \frac{4}{{12}} = \frac{{11}}{{12}}\)

Vậy \(\frac{3}{4} + \left( {\frac{1}{2} - \frac{1}{3}} \right)\) = \(\frac{3}{4} + \frac{1}{2} - \frac{1}{3}\)    

b)\(\frac{2}{3} - \left( {\frac{1}{2} + \frac{1}{3}} \right) = \frac{4}{6} - \left( {\frac{3}{6} + \frac{2}{6}} \right) = \frac{4}{6} - \frac{5}{6} = \frac{{ - 1}}{6}\)

 \(\frac{2}{3} - \frac{1}{2} - \frac{1}{3} = \frac{4}{6} - \frac{3}{6} - \frac{2}{6} = \frac{1}{6} - \frac{2}{6} = \frac{{ - 1}}{6}\)

Vậy \(\frac{2}{3} - \left( {\frac{1}{2} + \frac{1}{3}} \right)\)=\(\frac{2}{3} - \frac{1}{2} - \frac{1}{3}\).

`#3107`

`a)`

`3/4 + (1/2 - 1/3)`

`= 3/4 + (3/6 - 2/6)`

`= 3/4 + 1/6`

`= 11/12`

`3/4 + 1/2 - 1/3`

`= 9/12 + 6/12 - 4/12`

`= (9 + 6 - 4)/12`

`= 11/12`

Vì `11/12 = 11/12`

`=> 3/4 + (1/2 - 1/3) = 3/4 + 1/2 - 1/3`

`b)`

`2/3 - (1/2 + 1/3)`

`= 2/3 - (3/6 + 2/6)`

`= 2/3 - 5/6`

`= -1/6`

`2/3 - 1/2 - 1/3`

`= 4/6 - 3/6 - 2/6`

`= (4 - 3 - 2)/6`

`= -1/6`

Vì `-1/6 = -1/6`

`=> 2/3 - (1/2 + 1/3) = 2/3 - 1/2 - 1/3`

a/\(\frac{\left(2^3.5.7\right).\left(5^2.7^3\right)}{\left(2.5.7^2\right)^2}\)

=\(\frac{2^3.5^3.7^4}{2^2.5^2.7^4}\)

=2.5

=10

1 :\(\frac{7}{20}\)

2 \(\frac{1}{4}\)

3 \(\frac{23}{2}\)

4 2187

5 64

6 x=16

7 x=\(\frac{-1}{243}\)

8 mϵ∅

cho mình hỏi cài này là j vậy

Đề 2

1) \(\frac{7}{20}.\)

2) \(\frac{1}{4}.\)

3) \(\frac{23}{2}.\)

4) \(2187.\)

5) \(64.\)

6) \(x=16.\)

7) \(x=\left(-\frac{1}{3}\right)^5\)

8) \(m\in\varnothing.\)

Chúc bạn học tốt!

1, \(\frac{3}{5}+\left(-\frac{1}{4}\right)=\frac{12}{20}+\left(-\frac{5}{20}\right)=\frac{7}{20}\)

2,\(\left(-\frac{5}{18}\right)\left(-\frac{9}{10}\right)=\frac{-5.\left(-9\right)}{18.10}=\frac{45}{180}=\frac{1}{4}\)

3,\(4\frac{3}{5}:\frac{2}{5}=\frac{23}{5}.\frac{5}{2}=\frac{23}{2}\)