Solution - Power equations

Step  1  :

 1.1     33 = 3•11

(33)² = (3•11)² = 3² • 11²

Equation at the end of step  1  :

       6            
  (———————— • 4) -  2
   (32•112)         

Step  2  :

                6   
 Simplify   ————————
            (32•112)

Dividing exponents :

 2.1    3¹   divided by   3²   = 3^{(1 - 2)} = 3^(-1) = ¹/_3¹ = ¹/₃

Equation at the end of step  2  :

    2          
  (——— • 4) -  2
   363         

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  363  as the denominator :

         2     2 • 363
    2 =  —  =  ———————
         1       363  

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:

 8 - (2 • 363)     -718
 —————————————  =  ————
      363          363 

Final result :

  -718            
  ———— = -1.97796 
  363