Solution - Power equations

Step  1  :

 1.1     32 = 25

(32)² = (2⁵)² = 2¹⁰

Equation at the end of step  1  :

    1            
  (—— • 210) -  524288
   12            

Step  2  :

             1
 Simplify   ——
            12

Equation at the end of step  2  :

    1            
  (—— • 210) -  524288
   12            

Step  3  :

Dividing exponents :

 3.1    2¹⁰   divided by   2²   = 2^{(10 - 2)} = 2⁸

Equation at the end of step  3  :

  256    
  ——— -  524288
   3     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

              524288     524288 • 3
    524288 =  ——————  =  ——————————
                1            3     

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 :

 4.2       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:

 256 - (524288 • 3)     -1572608
 ——————————————————  =  ————————
         3                 3    

Final result :

  -1572608                 
  ———————— = -524202.66667 
     3