Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.12" was replaced by "(512/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  1  :

  512
  ——— • ((2)(-8)•(5)(-8))
  100

Step  2  :

            128
 Simplify   ———
            25 

Equation at the end of step  2  :

  128
  ——— • ((2)(-8)•(5)(-8))
  25 

Step  3  :

Multiplying exponents :

 3.1    5²  multiplied by  5⁸   = 5^{(2 + 8)} = 5¹⁰

Dividing exponents :

 3.2    2⁷   divided by   2⁸   = 2^{(7 - 8)} = 2^(-1) = ¹/_2¹ = ¹/₂

Final result :

     1                                     
  ——————— = 5.12000 • 10-8 
  (510•2)