Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): ".006" was replaced by "(006/1000)".

Step  1  :

             3 
 Simplify   ———
            500

Equation at the end of step  1  :

             3 
  (165-8) • ———
            500

Step  2  :

 2.1     165 = 3•5•11

(165)^-8 = (3•5•11)^(-8) = (3)^(-8) • (5)^(-8) • (11)^(-8)

Equation at the end of step  2  :

                                3 
  ((3)(-8)•(5)(-8)•(11)(-8)) • ———
                               500

Step  3  :

Multiplying exponents :

 3.1    5⁸  multiplied by  5³   = 5^{(8 + 3)} = 5¹¹

Dividing exponents :

 3.2    3¹   divided by   3⁸   = 3^{(1 - 8)} = 3^(-7) = ¹/_3⁷

Final result :

         1                                          
  ——————————————— = 1.09214 • 10-20 
  (37•511•118•22)