Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)¹⁸ = (2•5)¹⁸ = 2¹⁸ • 5¹⁸

Equation at the end of step  1  :

Step  2  :

 2.1     1000 = 23•53

(1000)⁷ = (2³•5³)⁷ = 2²¹ • 5²¹

Equation at the end of step  2  :

Step  3  :

            (221•521)
 Simplify   —————————
            (218•518)

Dividing exponents :

 3.1    2²¹   divided by   2¹⁸   = 2^{(21 - 18)} = 2³

Dividing exponents :

 3.2    5²¹   divided by   5¹⁸   = 5^{(21 - 18)} = 5³

Final result :

  1000