Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

Step  2  :

 2.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

Step  3  :

            (23•53)
 Simplify   ———————
            (26•56)

Dividing exponents :

 3.1    2³   divided by   2⁶   = 2^{(3 - 6)} = 2^(-3) = ¹/_2³

Dividing exponents :

 3.2    5³   divided by   5⁶   = 5^{(3 - 6)} = 5^(-3) = ¹/_5³

Final result :

    1            
  ———— = 0.00100 
  1000