Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.8" was replaced by "(68/10)". 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  :

   24         68
  (——•(104))-(——•(22•52))
   10         10

Step  2  :

            34
 Simplify   ——
            5 

Equation at the end of step  2  :

   24              34
  (—— • (104)) -  (—— • (22•52))
   10              5 

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Raising to a Power :

 3.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   24              
  (—— • (104)) -  680
   10              

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   24                 
  (—— • (24•54)) -  680
   10                 

Step  5  :

            12
 Simplify   ——
            5 

Equation at the end of step  5  :

   12                 
  (—— • (24•54)) -  680
   5                  

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

  (26•3•53) -  680

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   2⁶ • 3 • 5³ - 680  =   4 • (3 - 170) 

Final result :

  4 • (3 - 170)