Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.02" was replaced by "(102/100)". 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  :

   65         102
  (——•(105))•(———•(26•56))
   10         100

Step  2  :

            51
 Simplify   ——
            50

Equation at the end of step  2  :

   65             51
  (—— • (105)) • (—— • (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  :

   65
  (—— • (105)) • (3•17•25•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   65
  (—— • (25•55)) • (3•17•25•54)
   10

Step  5  :

            13
 Simplify   ——
            2 

Equation at the end of step  5  :

   13
  (—— • (25•55)) • (3•17•25•54)
   2 

Step  6  :

Dividing exponents :

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

Equation at the end of step  6  :

  (13•24•55) • (3•17•25•54)

Step  7  :

Multiplying exponents :

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

Multiplying exponents :

 7.2    5⁵  multiplied by  5⁴   = 5^{(5 + 4)} = 5⁹

Final result :

  (13•29•59•3•17)