Solution - Power equations

Step  1  :

 1.1     12 = 22•3

(12)⁷ = (2²•3)⁷ = 2¹⁴ • 3⁷

Equation at the end of step  1  :

Step  2  :

 2.1     12 = 22•3

(12)³ = (2²•3)³ = 2⁶ • 3³

Equation at the end of step  2  :

Step  3  :

             (26•33)
 Simplify   ————————
            (214•37)

Dividing exponents :

 3.1    2⁶   divided by   2¹⁴   = 2^{(6 - 14)} = 2^(-8) = ¹/_2⁸

Dividing exponents :

 3.2    3³   divided by   3⁷   = 3^{(3 - 7)} = 3^(-4) = ¹/_3⁴

Final result :

     1              
  ——————— = 0.00005 
  (28•34)