Solution - Power equations

Step  1  :

 1.1     125 = 53

(125)¹ = (5³)¹ = 5³

Equation at the end of step  1  :

  (1441)    53
  —————— -  ——
    2       3 

Step  2  :

            53
 Simplify   ——
            3 

Equation at the end of step  2  :

  (1441)    125
  —————— -  ———
    2        3 

Step  3  :

 3.1     144 = 24•32

(144)¹ = (2⁴•3²)¹ = 2⁴ • 3²

Equation at the end of step  3  :

  (24•32)    125
  ——————— -  ———
     2        3 

Step  4  :

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

Dividing exponents :

 4.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Equation at the end of step  4  :

        125
  72 -  ———
         3 

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

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

           72     72 • 3
     72 =  ——  =  ——————
           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 :

 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:

 72 • 3 - (125)     91
 ——————————————  =  ——
       3            3 

Final result :

  91            
  —— = 30.33333 
  3