Solution - Power equations

Step  1  :

 1.1     6 = 2•3

(6)⁵ = (2•3)⁵ = 2⁵ • 3⁵

Equation at the end of step  1  :

Step  2  :

 2.1     6 = 2•3

(6)³ = (2•3)³ = 2³ • 3³

Equation at the end of step  2  :

Step  3  :

            (23•33)
 Simplify   ———————
            (25•35)

Dividing exponents :

 3.1    2³   divided by   2⁵   = 2^{(3 - 5)} = 2^(-2) = ¹/_2²

Dividing exponents :

 3.2    3³   divided by   3⁵   = 3^{(3 - 5)} = 3^(-2) = ¹/_3²

Final result :

   1           
  —— = 0.02778 
  36