Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)²⁶ = (2•5)²⁶ = 2²⁶ • 5²⁶

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   —————————
            (226•526)

Dividing exponents :

 3.1    2²⁷   divided by   2²⁶   = 2^{(27 - 26)} = 2¹ = 2

Dividing exponents :

 3.2    5²⁷   divided by   5²⁶   = 5^{(27 - 26)} = 5¹ = 5

Final result :

  10