Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.12" was replaced by "(512/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  512
  ——— • ((2)(-5)•(5)(-5))
  100

Step  2  :

            128
 Simplify   ———
            25 

Equation at the end of step  2  :

  128
  ——— • ((2)(-5)•(5)(-5))
  25 

Step  3  :

Multiplying exponents :

 3.1    5²  multiplied by  5⁵   = 5^{(2 + 5)} = 5⁷

Dividing exponents :

 3.2    2⁷   divided by   2⁵   = 2^{(7 - 5)} = 2²

Final result :

   4           
  —— = 0.00005 
  57