Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.03" was replaced by "(03/100)".

Step  1  :

             3 
 Simplify   ———
            100

Equation at the end of step  1  :

                 3 
  5000 • ((1 +  ——— ÷ 12)60)
                100

Step  2  :

          3       
 Divide  ———  by  12
         100      

Equation at the end of step  2  :

                 1 
  5000 • ((1 +  ———)60)
                400

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  400  as the denominator :

          1     1 • 400
     1 =  —  =  ———————
          1       400  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 400 + 1     401
 ———————  =  ———
   400       400

Equation at the end of step  3  :

          401
  5000 • (———)60)
          400

Step  4  :

 4.1     400 = 2⁴•5² (400)⁶⁰ = (2⁴•5²)⁶⁰ = 2²⁴⁰ • 5¹²⁰

Equation at the end of step  4  :

            40160   
  5000 • ———————————
         (2240•5120) 

Step  5  :

Dividing exponents :

 5.1    2³   divided by   2²⁴⁰   = 2^{(3 - 240)} = 2^(-237) = ¹/_2²³⁷

Dividing exponents :

 5.2    5⁴   divided by   5¹²⁰   = 5^{(4 - 120)} = 5^(-116) = ¹/_5¹¹⁶

Final result :

     40160                 
  ——————————— = 5808.08391 
  (2237•5116)