Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.625" was replaced by "(625/1000)". 2 more similar replacement(s)

Step  1  :

            5
 Simplify   —
            8

Equation at the end of step  1  :

   602             5
  (——— • (1023)) • —
   100             8

Step  2  :

 2.1     10 = 2•5

(10)²³ = (2•5)²³ = 2²³ • 5²³

Equation at the end of step  2  :

   602                5
  (——— • (223•523)) • —
   100                8

Step  3  :

            301
 Simplify   ———
            50 

Equation at the end of step  3  :

   301                5
  (——— • (223•523)) • —
   50                 8

Step  4  :

Dividing exponents :

 4.1    2²³   divided by   2¹   = 2^{(23 - 1)} = 2²²

Dividing exponents :

 4.2    5²³   divided by   5²   = 5^{(23 - 2)} = 5²¹

Equation at the end of step  4  :

                   5
  (7•43•222•521) • —
                   8

Step  5  :

Multiplying exponents :

 5.1    5²¹  multiplied by  5¹   = 5^{(21 + 1)} = 5²²

Dividing exponents :

 5.2    2²²   divided by   2³   = 2^{(22 - 3)} = 2¹⁹

Final result :

  (7•43•219•522)