Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

Step  2  :

 2.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  2  :

Step  3  :

            (22•52)
 Simplify   ———————
            (25•55)

Dividing exponents :

 3.1    2²   divided by   2⁵   = 2^{(2 - 5)} = 2^(-3) = ¹/_2³

Dividing exponents :

 3.2    5²   divided by   5⁵   = 5^{(2 - 5)} = 5^(-3) = ¹/_5³

Final result :

    1            
  ———— = 0.00100 
  1000