Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.8" was replaced by "(78/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   814         78
  (———•(105))-(——•(22•52))
   100         10

Step  2  :

            39
 Simplify   ——
            5 

Equation at the end of step  2  :

   814              39
  (——— • (105)) -  (—— • (22•52))
   100              5 

Step  3  :

Raising to a Power :

 3.1    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   814              
  (——— • (105)) -  780
   100              

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   814                 
  (——— • (25•55)) -  780
   100                 

Step  5  :

            407
 Simplify   ———
            50 

Equation at the end of step  5  :

   407                 
  (——— • (25•55)) -  780
   50                  

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 6.2    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Equation at the end of step  6  :

  (11•37•24•53) -  780

Step  7  :

Final result :

  407 - 780