Solution - Power equations

Step  1  :

 1.1     100 = 22•52

(100)¹² = (2²•5²)¹² = 2²⁴ • 5²⁴

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   —————————
            (224•524)

Dividing exponents :

 3.1    2²⁷   divided by   2²⁴   = 2^{(27 - 24)} = 2³

Dividing exponents :

 3.2    5²⁷   divided by   5²⁴   = 5^{(27 - 24)} = 5³

Final result :

  1000