Solution - Power equations

Step  1  :

 1.1     568 = 23•71

(568)⁸ = (2³•71)⁸ = 2²⁴ • 71⁸

Equation at the end of step  1  :

Step  2  :

 2.1     568 = 23•71

(568)¹ = (2³•71)¹ = 2³ • 71

Equation at the end of step  2  :

  
 Step  3  :
 3.1     568 = 23•71

(568)¹ = (2³•71)¹ = 2³ • 71

Equation at the end of step  3  :

Step  4  :

             (23•71) 
 Simplify   —————————
            (227•719)

Dividing exponents :

 4.1    2³   divided by   2²⁷   = 2^{(3 - 27)} = 2^(-24) = ¹/_2²⁴

Dividing exponents :

 4.2    71¹   divided by   71⁹   = 71^{(1 - 9)} = 71^(-8) = ¹/_71⁸

Final result :

      1                                       
  ————————— = 9.23025 • 10-23 
  (224•718)