Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "7.5" was replaced by "(75/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  75
  —— • ((2)(-4)•(5)(-4))
  10

Step  2  :

            15
 Simplify   ——
            2 

Equation at the end of step  2  :

  15
  —— • ((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 :

    3            
  ———— = 0.00075 
  4000