Solution - Power equations

Step  1  :

 1.1     8 = 23

(8)² = (2³)² = 2⁶

Equation at the end of step  1  :

Step  2  :

 2.1     8 = 23

(8)⁵ = (2³)⁵ = 2¹⁵

Equation at the end of step  2  :

Step  3  :

            215
 Simplify   ———
            26 

Dividing exponents :

 3.1    2¹⁵   divided by   2⁶   = 2^{(15 - 6)} = 2⁹

Final result :

  512