Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8." was replaced by "(8/1)". 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  :

   16 8
  (——•—)•(211•511)
   10 1

Step  2  :

            8
 Simplify   —
            1

Equation at the end of step  2  :

   16   (108)
  (—— • —————) • (211•511)
   10     8  

Step  3  :

 3.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  3  :

   16   (28•58)
  (—— • ———————) • (211•511)
   10      8   

Step  4  :

            (28•58)
 Simplify   ———————
               8   

Dividing exponents :

 4.1    2⁸   divided by   2³   = 2^{(8 - 3)} = 2⁵

Equation at the end of step  4  :

   16
  (—— • (25•58)) • (211•511)
   10

Step  5  :

            8
 Simplify   —
            5

Equation at the end of step  5  :

   8
  (— • (25•58)) • (211•511)
   5

Step  6  :

Multiplying exponents :

 6.1    2³  multiplied by  2⁵   = 2^{(3 + 5)} = 2⁸

Dividing exponents :

 6.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  6  :

  (28•57) • (211•511)

Step  7  :

Multiplying exponents :

 7.1    2⁸  multiplied by  2¹¹   = 2^{(8 + 11)} = 2¹⁹

Multiplying exponents :

 7.2    5⁷  multiplied by  5¹¹   = 5^{(7 + 11)} = 5¹⁸

Final result :

  (219•518)