Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.68" was replaced by "(268/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)²² = (2•5)²² = 2²² • 5²²

Equation at the end of step  1  :

   15 268
  (——•———)•(222•522)
   10 100

Step  2  :

            67
 Simplify   ——
            25

Equation at the end of step  2  :

   15   67
  (—— • ——) • (222•522)
   10   25

Step  3  :

 3.1     10 = 2•5

(10)²⁰ = (2•5)²⁰ = 2²⁰ • 5²⁰

Equation at the end of step  3  :

   15   67
  (—— • ——) • (222•522)
   10   25

Step  4  :

                        67
 Divide  (220•520)  by  ——
                        25

Multiplying exponents :

 4.1    5²⁰  multiplied by  5²   = 5^{(20 + 2)} = 5²²

Equation at the end of step  4  :

   15   (220•522) 
  (—— • —————————) • (222•522)
   10      67    

Step  5  :

            3
 Simplify   —
            2

Equation at the end of step  5  :

   3   (220•522) 
  (— • —————————) • (222•522)
   2      67    

Step  6  :

Dividing exponents :

 6.1    2²⁰   divided by   2¹   = 2^{(20 - 1)} = 2¹⁹

Equation at the end of step  6  :

  (3•219•522) 
  ——————————— • (222•522)
      67     

Step  7  :

Multiplying exponents :

 7.1    2¹⁹  multiplied by  2²²   = 2^{(19 + 22)} = 2⁴¹

Multiplying exponents :

 7.2    5²²  multiplied by  5²²   = 5^{(22 + 22)} = 5⁴⁴

Final result :

  (3•241•544)                                   
  ——————————— = 5.59701 • 1041 
      67