Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

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

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

  456
  ——— • ((2)(-3)•(5)(-3))
  100

Step  2  :

            114
 Simplify   ———
            25 

Equation at the end of step  2  :

  114
  ——— • ((2)(-3)•(5)(-3))
  25 

Step  3  :

Multiplying exponents :

 3.1    5²  multiplied by  5³   = 5^{(2 + 3)} = 5⁵

Dividing exponents :

 3.2    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Final result :

     57             
  ——————— = 0.00456 
  (55•22)