Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.06" was replaced by "(06/100)".

Step  1  :

             3
 Simplify   ——
            50

Equation at the end of step  1  :

                  3
  10000 • ((1 +  —— ÷ 4)16)
                 50

Step  2  :

          3      
 Divide  ——  by  4
         50      

Equation at the end of step  2  :

                  3 
  10000 • ((1 +  ———)16)
                 200

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  200  as the denominator :

          1     1 • 200
     1 =  —  =  ———————
          1       200  

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:

 200 + 3     203
 ———————  =  ———
   200       200

Equation at the end of step  3  :

           203
  10000 • (———)16)
           200

Step  4  :

 4.1     203 = 7•29

(203)¹⁶ = (7•29)¹⁶ = 7¹⁶ • 29¹⁶  4.2     200 = 2³•5² (200)¹⁶ = (2³•5²)¹⁶ = 2⁴⁸ • 5³²

Equation at the end of step  4  :

          (716•2916)
  10000 • ——————————
          (248•532) 

Step  5  :

Dividing exponents :

 5.1    2⁴   divided by   2⁴⁸   = 2^{(4 - 48)} = 2^(-44) = ¹/_2⁴⁴

Dividing exponents :

 5.2    5⁴   divided by   5³²   = 5^{(4 - 32)} = 5^(-28) = ¹/_5²⁸

Final result :

  (716•2916)               
  —————————— = 12689.85548 
  (244•528)