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)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

Step  3  :

            (23•53)
 Simplify   ———————
            (27•57)

Dividing exponents :

 3.1    2³   divided by   2⁷   = 2^{(3 - 7)} = 2^(-4) = ¹/_2⁴

Dividing exponents :

 3.2    5³   divided by   5⁷   = 5^{(3 - 7)} = 5^(-4) = ¹/_5⁴

Final result :

     1              
  ——————— = 0.00010 
  (24•54)