Solution - Power equations

Step  1  :

 1.1     6 = 2•3

(6)²⁴ = (2•3)²⁴ = 2²⁴ • 3²⁴

Equation at the end of step  1  :

Step  2  :

 2.1     6 = 2•3

(6)¹⁷ = (2•3)¹⁷ = 2¹⁷ • 3¹⁷

Equation at the end of step  2  :

Step  3  :

            (217•317)
 Simplify   —————————
            (224•324)

Dividing exponents :

 3.1    2¹⁷   divided by   2²⁴   = 2^{(17 - 24)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 3.2    3¹⁷   divided by   3²⁴   = 3^{(17 - 24)} = 3^(-7) = ¹/_3⁷

Final result :

     1                                     
  ——————— = 3.57225 • 10-6 
  (27•37)