Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.854" was replaced by "(8854/1000)".

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

     8854            22
  (((————•(1012))•4)•——)•(27•57)
     1000            7 

Step  2  :

            22
 Simplify   ——
            7 

Equation at the end of step  2  :

     8854            22
  (((————•(1012))•4)•——)•(27•57)
     1000            7 

Step  3  :

 3.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  3  :

     8854                     22
  (((———— • (212•512)) • 4) • ——) • (27•57)
     1000                     7 

Step  4  :

            4427
 Simplify   ————
            500 

Equation at the end of step  4  :

     4427                     22
  (((———— • (212•512)) • 4) • ——) • (27•57)
     500                      7 

Step  5  :

Dividing exponents :

 5.1    2¹²   divided by   2²   = 2^{(12 - 2)} = 2¹⁰

Dividing exponents :

 5.2    5¹²   divided by   5³   = 5^{(12 - 3)} = 5⁹

Equation at the end of step  5  :

                           22
  (((19•233•210•59) • 4) • ——) • (27•57)
                           7 

Step  6  :

Multiplying exponents :

 6.1    2¹⁰  multiplied by  2²   = 2^{(10 + 2)} = 2¹²

Equation at the end of step  6  :

                     22
  ((19•233•212•59) • ——) • (27•57)
                     7 

Step  7  :

Multiplying exponents :

 7.1    2¹²  multiplied by  2¹   = 2^{(12 + 1)} = 2¹³

Equation at the end of step  7  :

  (19•233•213•59•11) 
  —————————————————— • (27•57)
          7         

Step  8  :

Multiplying exponents :

 8.1    2¹³  multiplied by  2⁷   = 2^{(13 + 7)} = 2²⁰

Multiplying exponents :

 8.2    5⁹  multiplied by  5⁷   = 5^{(9 + 7)} = 5¹⁶

Final result :

  (19•233•220•516•11)                                   
  ——————————————————— = 1.11307 • 1021 
           7