Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.54" was replaced by "(454/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

   68         454
  (——•(103))•(———•(26•56))
   10         100

Step  2  :

            227
 Simplify   ———
            50 

Equation at the end of step  2  :

   68             227
  (—— • (103)) • (——— • (26•56))
   10             50 

Step  3  :

Dividing exponents :

 3.1    2⁶   divided by   2¹   = 2^{(6 - 1)} = 2⁵

Raising to a Power :

 3.2    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Equation at the end of step  3  :

   68
  (—— • (103)) • (227•25•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   68
  (—— • (23•53)) • (227•25•54)
   10

Step  5  :

            34
 Simplify   ——
            5 

Equation at the end of step  5  :

   34
  (—— • (23•53)) • (227•25•54)
   5 

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Dividing exponents :

 6.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  6  :

  6800 • (227•25•54)

Step  7  :

Multiplying exponents :

 7.1    2⁴  multiplied by  2⁵   = 2^{(4 + 5)} = 2⁹

Multiplying exponents :

 7.2    5²  multiplied by  5⁴   = 5^{(2 + 4)} = 5⁶

Final result :

  (29•56•17•227)