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)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

   39         68
  (——•(104))•(——•(25•55))
   10         10

Step  2  :

            34
 Simplify   ——
            5 

Equation at the end of step  2  :

   39             34
  (—— • (104)) • (—— • (25•55))
   10             5 

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Raising to a Power :

 3.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  3  :

   39
  (—— • (104)) • (26•17•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   39
  (—— • (24•54)) • (26•17•54)
   10

Step  5  :

            39
 Simplify   ——
            10

Equation at the end of step  5  :

   39
  (—— • (24•54)) • (26•17•54)
   10

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

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

Equation at the end of step  6  :

  (3•13•23•53) • (26•17•54)

Step  7  :

Multiplying exponents :

 7.1    2³  multiplied by  2⁶   = 2^{(3 + 6)} = 2⁹

Multiplying exponents :

 7.2    5³  multiplied by  5⁴   = 5^{(3 + 4)} = 5⁷

Final result :

  (3•13•29•57•17)