Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "6.25" was replaced by "(625/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  625
  ——— • ((2)(-5)•(5)(-5))
  100

Step  2  :

            25
 Simplify   ——
            4 

Equation at the end of step  2  :

  25
  —— • ((2)(-5)•(5)(-5))
  4 

Step  3  :

Multiplying exponents :

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

Dividing exponents :

 3.2    5²   divided by   5⁵   = 5^{(2 - 5)} = 5^(-3) = ¹/_5³

Final result :

     1              
  ——————— = 0.00006 
  (27•53)