Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.45" was replaced by "(645/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  1  :

   35       645
  (——•(102))———•(210•510))
   10(      100

Step  2  :

            129
 Simplify   ———
            20 

Equation at the end of step  2  :

   35             129
  (—— • (102)) ÷ (——— • (210•510))
   10             20 

Step  3  :

Dividing exponents :

 3.1    2¹⁰   divided by   2²   = 2^{(10 - 2)} = 2⁸

Raising to a Power :

 3.2    5¹⁰   divided by   5¹   = 5^{(10 - 1)} = 5⁹

Equation at the end of step  3  :

   35
  (—— • (102)) ÷ (3•43•28•59)
   10

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   35
  (—— • (22•52)) ÷ (3•43•28•59)
   10

Step  5  :

            7
 Simplify   —
            2

Equation at the end of step  5  :

  7
  — • (22•52)) ÷ (3•43•28•59)
  2

Step  6  :

Dividing exponents :

 6.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Equation at the end of step  6  :

Step  7  :

                 350    
 Simplify   ————————————
            (3•43•28•59)

Dividing exponents :

 7.1    2¹   divided by   2⁸   = 2^{(1 - 8)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 7.2    5²   divided by   5⁹   = 5^{(2 - 9)} = 5^(-7) = ¹/_5⁷

Final result :

        7                                       
  ———————————— = 5.42636 • 10-9 
  (3•43•27•57)