Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "8.16" was replaced by "(816/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  816
  ——— • ((2)(-3)•(5)(-3))
  100

Step  2  :

            204
 Simplify   ———
            25 

Equation at the end of step  2  :

  204
  ——— • ((2)(-3)•(5)(-3))
  25 

Step  3  :

Multiplying exponents :

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

Dividing exponents :

 3.2    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Final result :

   51            
  ———— = 0.00816 
  6250