Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.02" was replaced by "(602/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)²³ = (2•5)²³ = 2²³ • 5²³

Equation at the end of step  1  :

   785        602
  (———•(1026))———•(223•523))
   100(       100

Step  2  :

            301
 Simplify   ———
            50 

Equation at the end of step  2  :

   785              301
  (——— • (1026)) ÷ (——— • (223•523))
   100              50 

Step  3  :

Dividing exponents :

 3.1    2²³   divided by   2¹   = 2^{(23 - 1)} = 2²²

Raising to a Power :

 3.2    5²³   divided by   5²   = 5^{(23 - 2)} = 5²¹

Equation at the end of step  3  :

   785
  (——— • (1026)) ÷ (7•43•222•521)
   100

Step  4  :

 4.1     10 = 2•5

(10)²⁶ = (2•5)²⁶ = 2²⁶ • 5²⁶

Equation at the end of step  4  :

   785
  (——— • (226•526)) ÷ (7•43•222•521)
   100

Step  5  :

            157
 Simplify   ———
            20 

Equation at the end of step  5  :

  157
  ——— • (226•526)) ÷ (7•43•222•521)
  20 

Step  6  :

Dividing exponents :

 6.1    2²⁶   divided by   2²   = 2^{(26 - 2)} = 2²⁴

Dividing exponents :

 6.2    5²⁶   divided by   5¹   = 5^{(26 - 1)} = 5²⁵

Equation at the end of step  6  :

Step  7  :

             (157•224•525)
 Simplify   ——————————————
            (7•43•222•521)

Dividing exponents :

 7.1    2²⁴   divided by   2²²   = 2^{(24 - 22)} = 2²

Dividing exponents :

 7.2    5²⁵   divided by   5²¹   = 5^{(25 - 21)} = 5⁴

Final result :

  (157•22•54)              
  ——————————— = 1303.98671 
      301