Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

    5
  {——}2 ÷ (23•53)
   17

Step  2  :

             5
 Simplify   ——
            17

Equation at the end of step  2  :

  (5
 (——)2) ÷ (23•53)
  17

Step  3  :

Equation at the end of step  3  :

   52
  ——— ÷ (23•53)
  172

Step  4  :

          52      
 Divide  ———  by  (23•53)
         172      

Dividing exponents :

 4.1    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

       1               
  —————————— = 0.00009 
  (172•23•5)