Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "9.19" was replaced by "(919/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-5 = (2•5)^(-5) = (2)^(-5) • (5)^(-5)

Equation at the end of step  1  :

   919
  (——— • ((2)(-5)•(5)(-5))) • 5
   100

Step  2  :

            919
 Simplify   ———
            100

Equation at the end of step  2  :

   919
  (——— • ((2)(-5)•(5)(-5))) • 5
   100

Step  3  :

Multiplying exponents :

 3.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Multiplying exponents :

 3.2    5²  multiplied by  5⁵   = 5^{(2 + 5)} = 5⁷

Equation at the end of step  3  :

    919  
  ——————— • 5
  (27•57)

Step  4  :

Dividing exponents :

 4.1    5¹   divided by   5⁷   = 5^{(1 - 7)} = 5^(-6) = ¹/_5⁶

Final result :

    919             
  ——————— = 0.00046 
  (27•56)