Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.08" was replaced by "(108/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)²⁷ = (2•5)²⁷ = 2²⁷ • 5²⁷

Equation at the end of step  1  :

   596 108
  (———•———)•(227•527)
   100 100

Step  2  :

            27
 Simplify   ——
            25

Equation at the end of step  2  :

   596   27
  (——— • ——) • (227•527)
   100   25

Step  3  :

 3.1     10 = 2•5

(10)²⁷ = (2•5)²⁷ = 2²⁷ • 5²⁷

Equation at the end of step  3  :

   596   27
  (——— • ——) • (227•527)
   100   25

Step  4  :

                        27
 Divide  (227•527)  by  ——
                        25

Multiplying exponents :

 4.1    5²⁷  multiplied by  5²   = 5^{(27 + 2)} = 5²⁹

Equation at the end of step  4  :

   596   (227•529) 
  (——— • —————————) • (227•527)
   100      27    

Step  5  :

            149
 Simplify   ———
            25 

Equation at the end of step  5  :

   149   (227•529) 
  (——— • —————————) • (227•527)
   25       27    

Step  6  :

Dividing exponents :

 6.1    5²⁹   divided by   5²   = 5^{(29 - 2)} = 5²⁷

Equation at the end of step  6  :

  (149•227•527) 
  ————————————— • (227•527)
       27      

Step  7  :

Multiplying exponents :

 7.1    2²⁷  multiplied by  2²⁷   = 2^{(27 + 27)} = 2⁵⁴

Multiplying exponents :

 7.2    5²⁷  multiplied by  5²⁷   = 5^{(27 + 27)} = 5⁵⁴

Final result :

  (149•254•554)                                   
  ————————————— = 5.51852 • 1054 
       27