Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "95.623" was replaced by "(95623/1000)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   95623
  (————— • (102)) • (22•52)
   1000 

Step  2  :

 2.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  2  :

   95623
  (————— • (22•52)) • (22•52)
   1000 

Step  3  :

            95623
 Simplify   —————
            1000 

Equation at the end of step  3  :

   95623
  (————— • (22•52)) • (22•52)
   1000 

Step  4  :

Dividing exponents :

 4.1    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 4.2    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  4  :

  (11•8693)
  ————————— • (22•52)
     10    

Step  5  :

Dividing exponents :

 5.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Dividing exponents :

 5.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Final result :

  (11•8693•2•5)