Solution - Power equations

Step  1  :

 1.1     6 = 2•3

(6)² = (2•3)² = 2² • 3²

Equation at the end of step  1  :

Step  2  :

 2.1     6 = 2•3

(6)⁵ = (2•3)⁵ = 2⁵ • 3⁵

Equation at the end of step  2  :

Step  3  :

            (25•35)
 Simplify   ———————
            (22•32)

Dividing exponents :

 3.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 3.2    3⁵   divided by   3²   = 3^{(5 - 2)} = 3³

Final result :

  216