Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

Step  2  :

              8100 
 Simplify   ———————
            (24•54)

Dividing exponents :

 2.1    2²   divided by   2⁴   = 2^{(2 - 4)} = 2^(-2) = ¹/_2²

Dividing exponents :

 2.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Final result :

   81           
  ——— = 0.81000 
  100