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4³³³ = (4³)¹¹¹ = 64¹¹¹

3⁴⁴⁴ = (3⁴)¹¹¹ = 81¹¹¹

Vì 64¹¹¹ < 81¹¹¹ nên 4³³³ < 3⁴⁴⁴ 

`2/5x-1/3=3/5x-2/3`

`2/5x-3/5x=-2/3+1/3`

`-1/5x=-1/3`

`x=-1/3:(-1/5)`

`x=5/3`

-5

123/100 = 1,23

1,23

Ta có :

\(ad=bc\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a}{2c}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a}{2c}=\dfrac{2a-b}{2c-d}\)

\(\Rightarrow\left(\dfrac{a}{c}\right)^7=\left(\dfrac{b}{d}\right)^7=\left(\dfrac{2a-b}{2c-d}\right)^7\)

\(\Rightarrow\dfrac{a^7}{c^7}=\dfrac{b^7}{d^7}=\dfrac{\left(2a-b\right)^7}{\left(2c-d\right)^7}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\dfrac{a^7}{c^7}=\dfrac{b^7}{d^7}=\dfrac{\left(2a-b\right)^7}{\left(2c-d\right)^7}=\dfrac{a^7-b^7}{c^7-d^7}\)

Lời giải:
\((\frac{-1}{6})^{100}=\frac{1}{6^{100}}\)

\((\frac{-1}{2})^{500}=\frac{1}{2^{500}}=\frac{1}{(2^5)^{100}}=\frac{1}{32^{100}}\)

Ta thấy: $6< 32\Rightarrow 6^{100}< 32^{100}$

$\Rightarrow \frac{1}{6^{100}}> \frac{1}{32^{100}}$

$\Rightarrow (\frac{-1}{6})^{100}> (\frac{-1}{2})^{500}$

(x-1)² = (2x -3)²

(x-1)² - (2x - 3)²  = 0

(x-1 - 2x +3)( x-1+ 2x -3) = 0

 ( -x + 2)(3x -4) = 0

⇔ \(\left[{}\begin{matrix}-x+2=0\\3x-4=0\end{matrix}\right.\)

⇔ \(\left[{}\begin{matrix}x=2\\x=\dfrac{4}{3}\end{matrix}\right.\)

x-1 mũ 2 = 123 

chuacs bạn học tốt

`[59-x]/41+[57-x]/43+[55-x]/45+[53-x]/47+[51-x]/49=-5`

`=>[59-x]/41+1+[57-x]/43+1+[55-x]/45+1+[53-x]/47+1+[51-x]/49+1=0`

`=>[100-x]/41+[100-x]/43+[100-x]/45+[100-x]/47+[100-x]/49=0`

`=>(100-x)(1/41+1/43+1/45+1/47+/49)=0`

  Mà `1/41+1/43+1/45+1/47+1/49 \ne 0`

  `=>100-x=0`

   `=>x=100`

`<=>(59-x)/41+1+(57-x)/43+1+(55-x)/45 +1+(53-x)/45 +1+(51-x)/49 +1 =0`

`<=> (100-x)/41 +  (100-x)/43+  (100-x)/45 + (100-x)/47 +  (100-x)/49 =0`

`<=>  (100-x) =0`

`<=>  (100-x) =0 [ do :1/41 + 1/43 +1/45 +1/47 +1/49 ne 0 ]`

`x = 100`

Vậy `x =100` 

( \(\dfrac{1}{7}\))⁵.7⁶ = \(\dfrac{7^6}{7^5}\) = 7^6-5 = 7