Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (3 • (105)) • (6 • ((2)(-8)•(5)(-8)))

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Equation at the end of step  2  :

                   3   
  (3 • (105)) • ———————
                (27•58)

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

                     3   
  (3 • (25•55)) • ———————
                  (27•58)

Step  4  :

Equation at the end of step  4  :

                 3   
  (3•25•55) • ———————
              (27•58)

Step  5  :

Multiplying exponents :

 5.1    3¹  multiplied by  3¹   = 3^{(1 + 1)} = 3²

Dividing exponents :

 5.2    2⁵   divided by   2⁷   = 2^{(5 - 7)} = 2^(-2) = ¹/_2²

Dividing exponents :

 5.3    5⁵   divided by   5⁸   = 5^{(5 - 8)} = 5^(-3) = ¹/_5³

Final result :

   9            
  ——— = 0.01800 
  500