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)⁷ = (2•3)⁷ = 2⁷ • 3⁷

Equation at the end of step  2  :

Step  3  :

            (27•37)
 Simplify   ———————
            (25•35)

Dividing exponents :

 3.1    2⁷   divided by   2⁵   = 2^{(7 - 5)} = 2²

Dividing exponents :

 3.2    3⁷   divided by   3⁵   = 3^{(7 - 5)} = 3²

Final result :

  36