Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (2 • (108)) • (3 • ((2)(-5)•(5)(-5)))

Step  2  :

Equation at the end of step  2  :

                   3   
  (2 • (108)) • ———————
                (25•55)

Step  3  :

 3.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  3  :

                     3   
  (2 • (28•58)) • ———————
                  (25•55)

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2⁸   = 2^{(1 + 8)} = 2⁹

Equation at the end of step  4  :

               3   
  (29•58) • ———————
            (25•55)

Step  5  :

Dividing exponents :

 5.1    2⁹   divided by   2⁵   = 2^{(9 - 5)} = 2⁴

Dividing exponents :

 5.2    5⁸   divided by   5⁵   = 5^{(8 - 5)} = 5³

Final result :

  6000