Solution - Power equations

Step  1  :

 1.1     100 = 22•52

(100)⁸ = (2²•5²)⁸ = 2¹⁶ • 5¹⁶

Equation at the end of step  1  :

Step  2  :

 2.1     100 = 22•52

(100)¹² = (2²•5²)¹² = 2²⁴ • 5²⁴

Equation at the end of step  2  :

Step  3  :

            (224•524)
 Simplify   —————————
            (216•516)

Dividing exponents :

 3.1    2²⁴   divided by   2¹⁶   = 2^{(24 - 16)} = 2⁸

Dividing exponents :

 3.2    5²⁴   divided by   5¹⁶   = 5^{(24 - 16)} = 5⁸

Final result :

  (28•58)