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¿Cómo vas a descomponer esta cbrt((b^(1/2))/(sqrt(27*b^3))*(1/(b^-2))^(1/8)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
        __________________________
       /     ___           ______ 
      /    \/ b           /  1    
     /   ----------*     /  ----  
    /       _______     /   /1 \  
   /       /     3     /    |--|  
3 /      \/  27*b   8 /     | 2|  
\/                  \/      \b /  
$$\sqrt[3]{\frac{\sqrt{b}}{\sqrt{27 b^{3}}} \sqrt[8]{\frac{1}{\frac{1}{b^{2}}}}}$$
((sqrt(b)/sqrt(27*b^3))*(1/(b^(-2)))^(1/8))^(1/3)
Simplificación general [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Descomposición de una fracción [src]
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
Respuesta numérica [src]
0.577350269189626*(b^0.5*(b^2)^0.125*(b^3)^(-0.5))^0.333333333333333
0.577350269189626*(b^0.5*(b^2)^0.125*(b^3)^(-0.5))^0.333333333333333
Compilar la expresión [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Denominador común [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Parte trigonométrica [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Combinatoria [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Potencias [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Denominador racional [src]
             _________________
            /    ____    ____ 
           /  8 /  2    /  3  
  ___     /   \/  b  *\/  b   
\/ 3 *   /    --------------- 
      3 /            5/2      
      \/            b         
------------------------------
              3               
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt[8]{b^{2}} \sqrt{b^{3}}}{b^{\frac{5}{2}}}}}{3}$$
sqrt(3)*((b^2)^(1/8)*sqrt(b^3)/b^(5/2))^(1/3)/3
Unión de expresiones racionales [src]
              _______________
             /          ____ 
            /    ___ 8 /  2  
  ___      /   \/ b *\/  b   
\/ 3 *    /    ------------- 
         /           ____    
      3 /           /  3     
      \/          \/  b      
-----------------------------
              3              
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{b^{2}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(b^2)^(1/8)/sqrt(b^3))^(1/3)/3
Abrimos la expresión [src]
                  _____________________
                 /              ______ 
                /    ___       /  1    
               /   \/ b *     /  ----  
              /              /   /1 \  
             /              /    |--|  
            /            8 /     | 2|  
  ___      /             \/      \b /  
\/ 3 *    /        ------------------- 
         /                  ____       
      3 /                  /  3        
      \/                 \/  b         
---------------------------------------
                   3                   
$$\frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{b} \sqrt[8]{\frac{1}{\frac{1}{b^{2}}}}}{\sqrt{b^{3}}}}}{3}$$
sqrt(3)*(sqrt(b)*(1/(b^(-2)))^(1/8)/sqrt(b^3))^(1/3)/3