Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "4.56" was replaced by "(456/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  456
  ——— • ((2)(-4)•(5)(-4))
  100

Step  2  :

            114
 Simplify   ———
            25 

Equation at the end of step  2  :

  114
  ——— • ((2)(-4)•(5)(-4))
  25 

Step  3  :

Multiplying exponents :

 3.1    5²  multiplied by  5⁴   = 5^{(2 + 4)} = 5⁶

Dividing exponents :

 3.2    2¹   divided by   2⁴   = 2^{(1 - 4)} = 2^(-3) = ¹/_2³

Final result :

     57             
  ——————— = 0.00046 
  (56•23)