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): "3.78" was replaced by "(378/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  378
  ——— • ((2)(-2)•(5)(-2))
  100

Step  2  :

            189
 Simplify   ———
            50 

Equation at the end of step  2  :

  189
  ——— • ((2)(-2)•(5)(-2))
  50 

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Multiplying exponents :

 3.2    5²  multiplied by  5²   = 5^{(2 + 2)} = 5⁴

Final result :

   189           
  ———— = 0.03780 
  5000