Solution - Power equations

Step  1  :

 1.1     27 = 33

(27)¹ = (3³)¹ = 3³

Equation at the end of step  1  :

  (91)    33
  ———— +  ——
   2      3 

Step  2  :

            33
 Simplify   ——
            3 

Raising to a Power :

 2.1    3³   divided by   3¹   = 3^{(3 - 1)} = 3²

Equation at the end of step  2  :

  (91)    
  ———— +  9
   2      

Step  3  :

 3.1     9 = 32

(9)¹ = (3²)¹ = 3²

Equation at the end of step  3  :

  32    
  —— +  9
  2     

Step  4  :

            32
 Simplify   ——
            2 

Equation at the end of step  4  :

  9    
  — +  9
  2    

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         9     9 • 2
    9 =  —  =  —————
         1       2  

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 :

 5.2       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:

 9 + 9 • 2     27
 —————————  =  ——
     2         2 

Final result :

  27            
  —— = 13.50000 
  2