Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.022" was replaced by "(6022/1000)". 3 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)²³ = (2•5)²³ = 2²³ • 5²³

Equation at the end of step  1  :

   239   4401 6022
  (——— ÷ ————•————)•(223•523)
   10    100  1000

Step  2  :

            3011
 Simplify   ————
            500 

Equation at the end of step  2  :

   239   4401   3011
  (——— ÷ ———— • ————) • (223•523)
   10    100    500 

Step  3  :

            4401
 Simplify   ————
            100 

Equation at the end of step  3  :

   239   4401   3011
  (——— ÷ ———— • ————) • (223•523)
   10    100    500 

Step  4  :

            239
 Simplify   ———
            10 

Equation at the end of step  4  :

   239   4401   3011
  (——— ÷ ———— • ————) • (223•523)
   10    100    500 

Step  5  :

         239      4401
 Divide  ———  by  ————
         10       100 

 5.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

239     4401       239      100
———  ÷  ————   =   ———  •  ————
10      100        10      4401

Equation at the end of step  5  :

   2390   3011
  (———— • ————) • (223•523)
   4401   500 

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2²³   = 2^{(1 + 23)} = 2²⁴

Multiplying exponents :

 6.2    5¹  multiplied by  5²³   = 5^{(1 + 23)} = 5²⁴

Dividing exponents :

 6.3    2²⁴   divided by   2²   = 2^{(24 - 2)} = 2²²

Dividing exponents :

 6.4    5²⁴   divided by   5³   = 5^{(24 - 3)} = 5²¹

Final result :

  (222•521•239•3011)                                   
  —————————————————— = 3.27030 • 1023 
         4401