Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.05" was replaced by "(05/100)".

Step  1  :

             1
 Simplify   ——
            20

Equation at the end of step  1  :

                  1
  10000 • ((1 +  —— ÷ 3)3)
                 20

Step  2  :

          1      
 Divide  ——  by  3
         20      

Equation at the end of step  2  :

                  1
  10000 • ((1 +  ——)3)
                 60

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  60  as the denominator :

          1     1 • 60
     1 =  —  =  ——————
          1       60  

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:

 60 + 1     61
 ——————  =  ——
   60       60

Equation at the end of step  3  :

           61
  10000 • (——)3)
           60

Step  4  :

 4.1     60 = 2²•3•5 (60)³ = (2²•3•5)³ = 2⁶ • 3³ • 5³

Equation at the end of step  4  :

              613   
  10000 • ——————————
          (26•33•53)

Step  5  :

Dividing exponents :

 5.1    2⁴   divided by   2⁶   = 2^{(4 - 6)} = 2^(-2) = ¹/_2²

Dividing exponents :

 5.2    5⁴   divided by   5³   = 5^{(4 - 3)} = 5¹ = 5

Final result :

  (5•613)               
  ——————— = 10508.37963 
    108