Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

Equation at the end of step  1  :

     ((63)3)  
  ————————————•(2)(-3)
  ((62)(44^2)) 

Step  2  :

 2.1     44 = 22•11

(44)² = (2²•11)² = 2⁴ • 11²

Equation at the end of step  2  :

       ((63)3)    
  ————————————————•(2)(-3)
  ((62)(2^4•11^2)) 

Step  3  :

 3.1     6 = 2•3

(6)² = (2•3)² = 2² • 3²

Equation at the end of step  3  :

        ((63)3)      
  ——————————————————— • (2)(-3)
  ((22•32)(2^4•11^2)) 
 Step  4  :
 4.1     6 = 2•3

(6)³ = (2•3)³ = 2³ • 3³

Equation at the end of step  4  :

    ((23•33)3) 
  ————————————— • (2)(-3)
  (23872•33872) 
 Step  5  :
               (29•39)   
 Simplify   —————————————
            (23872•33872) 

Dividing exponents :

 5.1    2⁹   divided by   2³⁸⁷²   = 2^{(9 - 3872)} = 2^(-3863) = ¹/_2³⁸⁶³

Dividing exponents :

 5.2    3⁹   divided by   3³⁸⁷²   = 3^{(9 - 3872)} = 3^(-3863) = ¹/_3³⁸⁶³

Equation at the end of step  5  :

        1      
  ————————————— • (2)(-3)
  (23863•33863) 

Step  6  :

Multiplying exponents :

 6.1    2³⁸⁶³  multiplied by  2³   = 2^{(3863 + 3)} = 2³⁸⁶⁶

Final result :

        1                                           
  ————————————— = 1.25496 • 10-3007 
  (23866•33863)