Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

Step  3  :

            (25•55)
 Simplify   ———————
            (27•57)

Dividing exponents :

 3.1    2⁵   divided by   2⁷   = 2^{(5 - 7)} = 2^(-2) = ¹/_2²

Dividing exponents :

 3.2    5⁵   divided by   5⁷   = 5^{(5 - 7)} = 5^(-2) = ¹/_5²

Final result :

   1            
  ——— = 0.01000 
  100