Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.07" was replaced by "(107/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹ = (2•5)¹ = 2 • 5

Equation at the end of step  1  :

   24       107
  (——•(105))———•(2•5))
   10(      100

Step  2  :

            107
 Simplify   ———
            100

Equation at the end of step  2  :

   24             107
  (—— • (105)) ÷ (——— • (2•5))
   10             100

Step  3  :

Dividing exponents :

 3.1    2¹   divided by   2²   = 2^{(1 - 2)} = 2^(-1) = ¹/_2¹ = ¹/₂

Raising to a Power :

 3.2    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

   24            107
  (—— • (105)) ÷ ———
   10            10 

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   24              107
  (—— • (25•55)) ÷ ———
   10              10 

Step  5  :

            12
 Simplify   ——
            5 

Equation at the end of step  5  :

  12              107
  —— • (25•55)) ÷ ———
  5               10 

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Dividing exponents :

 6.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

  107
  ———
  10 

Step  7  :

                        107
 Divide  (27•3•54)  by  ———
                        10 

Multiplying exponents :

 7.1    2⁷  multiplied by  2¹   = 2^{(7 + 1)} = 2⁸

Multiplying exponents :

 7.2    5⁴  multiplied by  5¹   = 5^{(4 + 1)} = 5⁵

Final result :

  (28•3•55)               
  ————————— = 22429.90654 
     107