Solution - Power equations

Step  1  :

 1.1     1000 = 23•53

(1000)¹² = (2³•5³)¹² = 2³⁶ • 5³⁶

Equation at the end of step  1  :

Step  2  :

 2.1     100 = 22•52

(100)²⁰ = (2²•5²)²⁰ = 2⁴⁰ • 5⁴⁰

Equation at the end of step  2  :

Step  3  :

            (240•540)
 Simplify   —————————
            (236•536)

Dividing exponents :

 3.1    2⁴⁰   divided by   2³⁶   = 2^{(40 - 36)} = 2⁴

Dividing exponents :

 3.2    5⁴⁰   divided by   5³⁶   = 5^{(40 - 36)} = 5⁴

Final result :

  (24•54)