Solution - Power equations

Step  1  :

 1.1     32 = 25

(32)¹ = (2⁵)¹ = 2⁵

Equation at the end of step  1  :

  (2001)    25
  —————— -  ——
    2       2 

Step  2  :

            25
 Simplify   ——
            2 

Raising to a Power :

 2.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Equation at the end of step  2  :

  (2001)    
  —————— -  16
    2       

Step  3  :

 3.1     200 = 23•52

(200)¹ = (2³•5²)¹ = 2³ • 5²

Equation at the end of step  3  :

  (23•52)    
  ——————— -  16
     2       

Step  4  :

            (23•52)
 Simplify   ———————
               2   

Dividing exponents :

 4.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  4  :

  100 -  16

Step  5  :

Final result :

  84