Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "3.9" was replaced by "(39/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   22         39
  (——•(109))•(——•((2)(-5)•(5)(-5)))
   10         10

Step  2  :

            39
 Simplify   ——
            10

Equation at the end of step  2  :

   22             39
  (—— • (109)) • (—— • ((2)(-5)•(5)(-5)))
   10             10

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Raising to a Power :

 3.2    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Equation at the end of step  3  :

   22               39  
  (—— • (109)) • ———————
   10            (26•56)

Step  4  :

 4.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  4  :

   22                 39  
  (—— • (29•59)) • ———————
   10              (26•56)

Step  5  :

            11
 Simplify   ——
            5 

Equation at the end of step  5  :

   11                 39  
  (—— • (29•59)) • ———————
   5               (26•56)

Step  6  :

Dividing exponents :

 6.1    5⁹   divided by   5¹   = 5^{(9 - 1)} = 5⁸

Equation at the end of step  6  :

                  39  
  (11•29•58) • ———————
               (26•56)

Step  7  :

Dividing exponents :

 7.1    2⁹   divided by   2⁶   = 2^{(9 - 6)} = 2³

Dividing exponents :

 7.2    5⁸   divided by   5⁶   = 5^{(8 - 6)} = 5²

Final result :

  (11•23•52•3•13)