Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "6.1" was replaced by "(61/10)".

Step  1  :

 1.1   Negative number raised to an even power is positive 

For example let's look at (-7)⁶ , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)⁶ can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)⁶ can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 7⁶ which is positive.

We proved that (-7)⁶ is equal to (7)⁶ which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

Equation at the end of step  1  :

   61
  {——}5^2
   10

Step  2  :

            61
 Simplify   ——
            10

Equation at the end of step  2  :

  61
 (——)5^2
  10

Step  3  :

 3.1     10 = 2•5 (10)²⁵ = (2•5)²⁵ = 2²⁵ • 5²⁵

Final result :

     6125                                    
  ————————— = 4.29780 • 1019 
  (225•525)