Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-11" was replaced by "^(-11)".

(2): "3.1" was replaced by "(31/10)".

Step  1  :

 1.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  1  :

   31
  (—— • (10-11)) • (29•59)
   10

Step  2  :

 2.1     10 = 2•5

(10)^-11 = (2•5)^(-11) = (2)^(-11) • (5)^(-11)

Equation at the end of step  2  :

   31
  (—— • ((2)(-11)•(5)(-11))) • (29•59)
   10

Step  3  :

            31
 Simplify   ——
            10

Equation at the end of step  3  :

   31
  (—— • ((2)(-11)•(5)(-11))) • (29•59)
   10

Step  4  :

Multiplying exponents :

 4.1    2¹  multiplied by  2¹¹   = 2^{(1 + 11)} = 2¹²

Multiplying exponents :

 4.2    5¹  multiplied by  5¹¹   = 5^{(1 + 11)} = 5¹²

Equation at the end of step  4  :

      31   
  ————————— • (29•59)
  (212•512) 

Step  5  :

Dividing exponents :

 5.1    2⁹   divided by   2¹²   = 2^{(9 - 12)} = 2^(-3) = ¹/_2³

Dividing exponents :

 5.2    5⁹   divided by   5¹²   = 5^{(9 - 12)} = 5^(-3) = ¹/_5³

Final result :

   31            
  ———— = 0.03100 
  1000