Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.035" was replaced by "(035/1000)".

Step  1  :

             7 
 Simplify   ———
            200

Equation at the end of step  1  :

                 7 
  1200 • ((1 +  ———)12)
                200

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   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 :

 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:

 200 + 7     207
 ———————  =  ———
   200       200

Equation at the end of step  2  :

          207
  1200 • (———)12)
          200

Step  3  :

 3.1     207 = 32•23

(207)¹² = (3²•23)¹² = 3²⁴ • 23¹²  3.2     200 = 2³•5² (200)¹² = (2³•5²)¹² = 2³⁶ • 5²⁴

Equation at the end of step  3  :

         (324•2312)
  1200 • ——————————
         (236•524) 

Step  4  :

Multiplying exponents :

 4.1    3¹  multiplied by  3²⁴   = 3^{(1 + 24)} = 3²⁵

Dividing exponents :

 4.2    2⁴   divided by   2³⁶   = 2^{(4 - 36)} = 2^(-32) = ¹/_2³²

Dividing exponents :

 4.3    5²   divided by   5²⁴   = 5^{(2 - 24)} = 5^(-22) = ¹/_5²²

Final result :

  (325•2312)              
  —————————— = 1813.28239 
  (232•522)