Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-24" was replaced by "^(-24)". 1 more similar replacement(s)

(2): "1.661" was replaced by "(1661/1000)". 2 more similar replacement(s)

Step  1  :

            1661
 Simplify   ————
            1000

Equation at the end of step  1  :

   266               1661
  (——— • (10-23)) • (————)-24)
   100               1000

Step  2  :

 2.1     1661 = 11•151

(1661)^-24 = (11•151)^(-24) = (11)^(-24) • (151)^(-24)  2.2     1000 = 2³•5³ (1000)^-24 = (2³•5³)^(-24) = (2)^(-72) • (5)^(-72)

Equation at the end of step  2  :

   266              ((11)(-24)•(151)(-24))
  (——— • (10-23)) • ——————————————————————
   100               ((2)(-72)•(5)(-72))  

Step  3  :

 3.1     10 = 2•5

(10)^-23 = (2•5)^(-23) = (2)^(-23) • (5)^(-23)

Equation at the end of step  3  :

   266                          ((11)(-24)•(151)(-24))
  (——— • ((2)(-23)•(5)(-23))) • ——————————————————————
   100                           ((2)(-72)•(5)(-72))  

Step  4  :

            133
 Simplify   ———
            50 

Equation at the end of step  4  :

   133                          ((11)(-24)•(151)(-24))
  (——— • ((2)(-23)•(5)(-23))) • ——————————————————————
   50                            ((2)(-72)•(5)(-72))  

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2²³   = 2^{(1 + 23)} = 2²⁴

Multiplying exponents :

 5.2    5²  multiplied by  5²³   = 5^{(2 + 23)} = 5²⁵

Equation at the end of step  5  :

     133      ((11)(-24)•(151)(-24))
  ————————— • ——————————————————————
  (224•525)     ((2)(-72)•(5)(-72))  

Step  6  :

Dividing exponents :

 6.1    2⁷²   divided by   2²⁴   = 2^{(72 - 24)} = 2⁴⁸

Dividing exponents :

 6.2    5⁷²   divided by   5²⁵   = 5^{(72 - 25)} = 5⁴⁷

Final result :

  (7•19•248•547)                                   
  —————————————— = 1.36776 • 10-28 
   (1124•15124)