Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.1" was replaced by "(51/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   51
  (—— • ((2)(-5)•(5)(-5))) • 2
   10

Step  2  :

            51
 Simplify   ——
            10

Equation at the end of step  2  :

   51
  (—— • ((2)(-5)•(5)(-5))) • 2
   10

Step  3  :

Multiplying exponents :

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

Multiplying exponents :

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

Equation at the end of step  3  :

     51  
  ——————— • 2
  (26•56)

Step  4  :

Dividing exponents :

 4.1    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Final result :

     51             
  ——————— = 0.00010 
  (25•56)