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
  35000 • ((1 -  ——)8)
                 20

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  20  as the denominator :

          1     1 • 20
     1 =  —  =  ——————
          1       20  

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 :

 2.2       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:

 20 - (1)     19
 ————————  =  ——
    20        20

Equation at the end of step  2  :

           19
  35000 • (——)8)
           20

Step  3  :

 3.1     20 = 2²•5 (20)⁸ = (2²•5)⁸ = 2¹⁶ • 5⁸

Equation at the end of step  3  :

             198  
  35000 • ————————
          (216•58)

Step  4  :

Dividing exponents :

 4.1    2³   divided by   2¹⁶   = 2^{(3 - 16)} = 2^(-13) = ¹/_2¹³

Dividing exponents :

 4.2    5⁴   divided by   5⁸   = 5^{(4 - 8)} = 5^(-4) = ¹/_5⁴

Final result :

   (7•198)               
  ———————— = 23219.71509 
  (213•54)