Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "4." was replaced by "(4/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

   43         4
  (——•(102))•(—•((2)(-3)•(5)(-3)))
   10         1

Step  2  :

            4
 Simplify   —
            1

Equation at the end of step  2  :

   43
  (—— • (102)) • (4 • ((2)(-3)•(5)(-3)))
   10

Step  3  :

Raising to a Power :

 3.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

   43             1 
  (—— • (102)) • ———
   10            250

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   43               1 
  (—— • (22•52)) • ———
   10              250

Step  5  :

            43
 Simplify   ——
            10

Equation at the end of step  5  :

   43               1 
  (—— • (22•52)) • ———
   10              250

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Dividing exponents :

 6.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  6  :

         1 
  430 • ———
        250

Step  7  :

Final result :

  43           
  —— = 1.72000 
  25