Solution - Power equations

Step  1  :

 1.1     64 = 26

(64)¹ = (2⁶)¹ = 2⁶

Equation at the end of step  1  :

  (1001)    26
  —————— -  ——
    2       6 

Step  2  :

            26
 Simplify   ——
            6 

Raising to a Power :

 2.1    2⁶   divided by   2¹   = 2^{(6 - 1)} = 2⁵

Equation at the end of step  2  :

  (1001)    32
  —————— -  ——
    2       3 

Step  3  :

 3.1     100 = 22•52

(100)¹ = (2²•5²)¹ = 2² • 5²

Equation at the end of step  3  :

  (22•52)    32
  ——————— -  ——
     2       3 

Step  4  :

            (22•52)
 Simplify   ———————
               2   

Dividing exponents :

 4.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Equation at the end of step  4  :

        32
  50 -  ——
        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 :

           50     50 • 3
     50 =  ——  =  ——————
           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:

 50 • 3 - (32)     118
 —————————————  =  ———
       3            3 

Final result :

  118            
  ——— = 39.33333 
   3