Выражение: 52root(n^4/8*m^2):52root(4*m^2/n)

Ответ: n^(1//13)/52root8/52root4*52rootn

Решаем по действиям:
1. 52root(n^4/8*m^2)=n^(1//13)/52root8*m^(1//26)
  52root(n^4/8*m^2)=52root(n^4)/52root8*52root(m^2)
  1.1. 52root(n^4)=n^(1//13)
  1.2. 52root(m^2)=m^(1//26)
2. 52root(4*m^2/n)=52root4*m^(1//26)/52rootn
3. n^(1//13)/52root8*m^(1//26):(52root4*m^(1//26)/52rootn)=n^(1//13)/52root8*m^(1//26)/52root4/m^(1//26)*52rootn
4. m^(1//26)/m^(1//26)=1

Решаем по шагам:
1. n^(1//13)/52root8*m^(1//26):52root(4*m^2/n)
  1.1. 52root(n^4/8*m^2)=n^(1//13)/52root8*m^(1//26)
      52root(n^4/8*m^2)=52root(n^4)/52root8*52root(m^2)
    1.1.1. 52root(n^4)=n^(1//13)
    1.1.2. 52root(m^2)=m^(1//26)
2. n^(1//13)/52root8*m^(1//26):(52root4*m^(1//26)/52rootn)
  2.1. 52root(4*m^2/n)=52root4*m^(1//26)/52rootn
3. n^(1//13)/52root8*m^(1//26)/52root4/m^(1//26)*52rootn
  3.1. n^(1//13)/52root8*m^(1//26):(52root4*m^(1//26)/52rootn)=n^(1//13)/52root8*m^(1//26)/52root4/m^(1//26)*52rootn
4. n^(1//13)/52root8/52root4*52rootn
  4.1. m^(1//26)/m^(1//26)=1

Приводим к окончательному ответу с возможной потерей точности:

  Окончательный ответ: n^0.0769230769230769/1.06891997265126*52rootn

  По действиям:
  1. 1//13~~0.0769230769230769
      1.00|1_3_ _
       9_1_|0.0769230769230769
        90
        7_8_
        120
        1_1_7_
          30
          2_6_
           40
           3_9_
            100
             9_1_
              90
              7_8_
              120
              1_1_7_
                30
                2_6_
                 40
                 3_9_
                  100
                   9_1_
                    90
                    7_8_
                    120
                    1_1_7_
                      3
  2. 52root8=1.04079959637863
  3. 52root4=1.02701805070877
  4. 1.04079959637863*1.02701805070877~~1.06891997265126
                   X1.04079959637863
       _ _ _ _ _ _ _ _ _ _ _ _ _ _1_._0_2_7_0_1_8_0_5_0_7_0_8_7_7_ _
                    728559717465041
                   728559717465041 
                  832639677102904  
                 000000000000000   
                728559717465041    
               000000000000000     
              520399798189315      
             000000000000000       
            832639677102904        
           104079959637863         
          000000000000000          
         728559717465041           
        208159919275726            
       000000000000000             
      1_0_4_0_7_9_9_5_9_6_3_7_8_6_3_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
      1.0689199726512551741967815851

  По шагам:
  1. n^0.0769230769230769/52root8/52root4*52rootn
    1.1. 1//13~~0.0769230769230769
          1.00|1_3_ _
           9_1_|0.0769230769230769
            90
            7_8_
            120
            1_1_7_
              30
              2_6_
               40
               3_9_
                100
                 9_1_
                  90
                  7_8_
                  120
                  1_1_7_
                    30
                    2_6_
                     40
                     3_9_
                      100
                       9_1_
                        90
                        7_8_
                        120
                        1_1_7_
                          3
  2. n^0.0769230769230769/1.04079959637863/52root4*52rootn
    2.1. 52root8=1.04079959637863
  3. n^0.0769230769230769/1.04079959637863/1.02701805070877*52rootn
    3.1. 52root4=1.02701805070877
  4. n^0.0769230769230769/1.06891997265126*52rootn
    4.1. 1.04079959637863*1.02701805070877~~1.06891997265126
                       X1.04079959637863
           _ _ _ _ _ _ _ _ _ _ _ _ _ _1_._0_2_7_0_1_8_0_5_0_7_0_8_7_7_ _
                        728559717465041
                       728559717465041 
                      832639677102904  
                     000000000000000   
                    728559717465041    
                   000000000000000     
                  520399798189315      
                 000000000000000       
                832639677102904        
               104079959637863         
              000000000000000          
             728559717465041           
            208159919275726            
           000000000000000             
          1_0_4_0_7_9_9_5_9_6_3_7_8_6_3_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
          1.0689199726512551741967815851