Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.6" was replaced by "(46/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

       46
  5 • (—— • ((2)(-5)•(5)(-5)))
       10

Step  2  :

            23
 Simplify   ——
            5 

Equation at the end of step  2  :

       23
  5 • (—— • ((2)(-5)•(5)(-5)))
       5 

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  3  :

         23  
  5 • ———————
      (56•25)

Step  4  :

Dividing exponents :

 4.1    5¹   divided by   5⁶   = 5^{(1 - 6)} = 5^(-5) = ¹/_5⁵

Final result :

     23             
  ——————— = 0.00023 
  (55•25)