Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

(2): "7.8" was replaced by "(78/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-2 = (2•5)^(-2) = (2)^(-2) • (5)^(-2)

Equation at the end of step  1  :

   78
  (—— • ((2)(-2)•(5)(-2)))5
   10

Step  2  :

            39
 Simplify   ——
            5 

Equation at the end of step  2  :

   39
  (—— • ((2)(-2)•(5)(-2)))5
   5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5²   = 5^{(1 + 2)} = 5³

Equation at the end of step  3  :

   39
 (———)5
  500

Step  4  :

 4.1     39 = 3•13

(39)⁵ = (3•13)⁵ = 3⁵ • 13⁵  4.2     500 = 2²•5³ (500)⁵ = (2²•5³)⁵ = 2¹⁰ • 5¹⁵

Final result :

   (35•135)                                  
  ————————— = 2.88717 • 10-6 
  (210•515)