Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-13" was replaced by "^(-13)".

(2): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹¹ = (2•5)¹¹ = 2¹¹ • 5¹¹

Equation at the end of step  1  :

   6           25
  (—•(10-13))•(——•(211•511))
   1           10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   6               5
  (— • (10-13)) • (— • (211•511))
   1               2

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5¹¹   = 5^{(1 + 11)} = 5¹²

Raising to a Power :

 3.2    2¹¹   divided by   2¹   = 2^{(11 - 1)} = 2¹⁰

Equation at the end of step  3  :

   6
  (— • (10-13)) • (512•210)
   1

Step  4  :

 4.1     10 = 2•5

(10)^-13 = (2•5)^(-13) = (2)^(-13) • (5)^(-13)

Equation at the end of step  4  :

   6
  (— • ((2)(-13)•(5)(-13))) • (512•210)
   1

Step  5  :

            6
 Simplify   —
            1

Equation at the end of step  5  :

  (6 • ((2)(-13)•(5)(-13))) • (512•210)

Step  6  :

Dividing exponents :

 6.1    2¹   divided by   2¹³   = 2^{(1 - 13)} = 2^(-12) = ¹/_2¹²

Equation at the end of step  6  :

      3    
  ————————— • (512•210)
  (212•513) 

Step  7  :

Dividing exponents :

 7.1    5¹²   divided by   5¹³   = 5^{(12 - 13)} = 5^(-1) = ¹/_5¹ = ¹/₅

Dividing exponents :

 7.2    2¹⁰   divided by   2¹²   = 2^{(10 - 12)} = 2^(-2) = ¹/_2²

Final result :

   3           
  —— = 0.15000 
  20