Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "4.13" was replaced by "(413/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

  413
  ——— • ((2)(-3)•(5)(-3))
  100

Step  2  :

            413
 Simplify   ———
            100

Equation at the end of step  2  :

  413
  ——— • ((2)(-3)•(5)(-3))
  100

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Multiplying exponents :

 3.2    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Final result :

    413             
  ——————— = 0.00413 
  (25•55)