Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.05" was replaced by "(105/100)". 2 more similar replacement(s)

Step  1  :

            21
 Simplify   ——
            20

Equation at the end of step  1  :

  50    21
  —— • (——)10)
  1     20

Step  2  :

 2.1     21 = 3•7

(21)¹⁰ = (3•7)¹⁰ = 3¹⁰ • 7¹⁰  2.2     20 = 2²•5 (20)¹⁰ = (2²•5)¹⁰ = 2²⁰ • 5¹⁰

Equation at the end of step  2  :

  50   (310•710)
  —— • —————————
  1    (220•510)

Step  3  :

            50
 Simplify   ——
            1 

Equation at the end of step  3  :

       (310•710)
  50 • —————————
       (220•510)

Step  4  :

Dividing exponents :

 4.1    2¹   divided by   2²⁰   = 2^{(1 - 20)} = 2^(-19) = ¹/_2¹⁹

Dividing exponents :

 4.2    5²   divided by   5¹⁰   = 5^{(2 - 10)} = 5^(-8) = ¹/_5⁸

Final result :

  (310•710)            
  ————————— = 81.44473 
  (219•58)