Solution - Power equations

Step  1  :

 1.1     144 = 24•32

(144)² = (2⁴•3²)² = 2⁸ • 3⁴

Equation at the end of step  1  :

Step  2  :

 2.1     144 = 24•32

(144)¹⁴ = (2⁴•3²)¹⁴ = 2⁵⁶ • 3²⁸

Equation at the end of step  2  :

Step  3  :

            (256•328)
 Simplify   —————————
             (28•34) 

Dividing exponents :

 3.1    2⁵⁶   divided by   2⁸   = 2^{(56 - 8)} = 2⁴⁸

Dividing exponents :

 3.2    3²⁸   divided by   3⁴   = 3^{(28 - 4)} = 3²⁴

Final result :

  (248•324)