Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.1" was replaced by "(21/10)". 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  :

   65         21
  (——•(103))•(——•(25•55))
   10         10

Step  2  :

            21
 Simplify   ——
            10

Equation at the end of step  2  :

   65             21
  (—— • (103)) • (—— • (25•55))
   10             10

Step  3  :

Dividing exponents :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Raising to a Power :

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

Equation at the end of step  3  :

   65
  (—— • (103)) • (3•7•24•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   65
  (—— • (23•53)) • (3•7•24•54)
   10

Step  5  :

            13
 Simplify   ——
            2 

Equation at the end of step  5  :

   13
  (—— • (23•53)) • (3•7•24•54)
   2 

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  6  :

  6500 • (3•7•24•54)

Step  7  :

Multiplying exponents :

 7.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Multiplying exponents :

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

Final result :

  (26•57•13•3•7)