Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.45" was replaced by "(45/100)".

Step  1  :

             9
 Simplify   ——
            20

Equation at the end of step  1  :

                9
  200 • ((1 +  ——)5)
               20

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to 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 + 9     29
 ——————  =  ——
   20       20

Equation at the end of step  2  :

         29
  200 • (——)5)
         20

Step  3  :

 3.1     20 = 2²•5 (20)⁵ = (2²•5)⁵ = 2¹⁰ • 5⁵

Equation at the end of step  3  :

           295  
  200 • ————————
        (210•55)

Step  4  :

Dividing exponents :

 4.1    2³   divided by   2¹⁰   = 2^{(3 - 10)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 4.2    5²   divided by   5⁵   = 5^{(2 - 5)} = 5^(-3) = ¹/_5³

Final result :

    295                
  ——————— = 1281.94681 
  (27•53)