Solution - Power equations

Step  1  :

            1
 Simplify   —
            3

Equation at the end of step  1  :

   (1441)          1
  (—————— • 64) -  —
     2             3

Step  2  :

 2.1     144 = 24•32

(144)¹ = (2⁴•3²)¹ = 2⁴ • 3²

Equation at the end of step  2  :

   (24•32)          1
  (——————— • 64) -  —
      2             3

Step  3  :

            (24•32)
 Simplify   ———————
               2   

Dividing exponents :

 3.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Equation at the end of step  3  :

               1
  (72 • 64) -  —
               3

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

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

             4608     4608 • 3
     4608 =  ————  =  ————————
              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:

 4608 • 3 - (1)     13823
 ——————————————  =  —————
       3              3  

Final result :

  13823              
  ————— = 4607.66667 
    3