Solution - Power equations

Step  1  :

 1.1     100 = 22•52

(100)⁴ = (2²•5²)⁴ = 2⁸ • 5⁸

Equation at the end of step  1  :

Step  2  :

 2.1     1000 = 23•53

(1000)⁹ = (2³•5³)⁹ = 2²⁷ • 5²⁷

Equation at the end of step  2  :

Step  3  :

            (227•527)
 Simplify   —————————
             (28•58) 

Dividing exponents :

 3.1    2²⁷   divided by   2⁸   = 2^{(27 - 8)} = 2¹⁹

Dividing exponents :

 3.2    5²⁷   divided by   5⁸   = 5^{(27 - 8)} = 5¹⁹

Final result :

  (219•519)