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  :

  (4 • (1010)) • (9 • ((2)(-5)•(5)(-5)))

Step  2  :

Equation at the end of step  2  :

                    9   
  (4 • (1010)) • ———————
                 (25•55)

Step  3  :

 3.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  3  :

                       9   
  (4 • (210•510)) • ———————
                    (25•55)

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2¹⁰   = 2^{(2 + 10)} = 2¹²

Equation at the end of step  4  :

                 9   
  (212•510) • ———————
              (25•55)

Step  5  :

Dividing exponents :

 5.1    2¹²   divided by   2⁵   = 2^{(12 - 5)} = 2⁷

Dividing exponents :

 5.2    5¹⁰   divided by   5⁵   = 5^{(10 - 5)} = 5⁵

Final result :

  (27•55•32)