Solution - Power equations

Step  1  :

 1.1     81 = 34

(81)³ = (3⁴)³ = 3¹²

Equation at the end of step  1  :

  (271)   312
  ————— • ———
    3      4 

Step  2  :

            312
 Simplify   ———
             4 

Equation at the end of step  2  :

  (271)   312
  ————— • ———
    3      4 

Step  3  :

 3.1     27 = 33

(27)¹ = (3³)¹ = 3³

Equation at the end of step  3  :

  33   312
  —— • ———
  3     4 

Step  4  :

            33
 Simplify   ——
            3 

Dividing exponents :

 4.1    3³   divided by   3¹   = 3^{(3 - 1)} = 3²

Equation at the end of step  4  :

      312
  9 • ———
       4 

Step  5  :

Multiplying exponents :

 5.1    3²  multiplied by  3¹²   = 3^{(2 + 12)} = 3¹⁴

Final result :

  314                                 
  ——— = 1.19574 • 106 
   4