Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

  25
  —— • ((2)(-4)•(5)(-4))
  10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

  5
  — • ((2)(-4)•(5)(-4))
  2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Dividing exponents :

 3.2    5¹   divided by   5⁴   = 5^{(1 - 4)} = 5^(-3) = ¹/_5³

Final result :

    1            
  ———— = 0.00025 
  4000