Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.1" was replaced by "(31/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹¹ = (2•5)¹¹ = 2¹¹ • 5¹¹

Equation at the end of step  1  :

   42         31
  (——•(106))•(——•(211•511))
   10         10

Step  2  :

            31
 Simplify   ——
            10

Equation at the end of step  2  :

   42             31
  (—— • (106)) • (—— • (211•511))
   10             10

Step  3  :

Dividing exponents :

 3.1    2¹¹   divided by   2¹   = 2^{(11 - 1)} = 2¹⁰

Raising to a Power :

 3.2    5¹¹   divided by   5¹   = 5^{(11 - 1)} = 5¹⁰

Equation at the end of step  3  :

   42
  (—— • (106)) • (31•210•510)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  4  :

   42
  (—— • (26•56)) • (31•210•510)
   10

Step  5  :

            21
 Simplify   ——
            5 

Equation at the end of step  5  :

   21
  (—— • (26•56)) • (31•210•510)
   5 

Step  6  :

Dividing exponents :

 6.1    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  6  :

  (3•7•26•55) • (31•210•510)

Step  7  :

Multiplying exponents :

 7.1    2⁶  multiplied by  2¹⁰   = 2^{(6 + 10)} = 2¹⁶

Multiplying exponents :

 7.2    5⁵  multiplied by  5¹⁰   = 5^{(5 + 10)} = 5¹⁵

Final result :

  (3•7•216•515•31)