Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 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  :

   781          25
  (———•(1011))•(——•(211•511))
   100          10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   781              5
  (——— • (1011)) • (— • (211•511))
   100              2

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5¹¹   = 5^{(1 + 11)} = 5¹²

Raising to a Power :

 3.2    2¹¹   divided by   2¹   = 2^{(11 - 1)} = 2¹⁰

Equation at the end of step  3  :

   781
  (——— • (1011)) • (512•210)
   100

Step  4  :

 4.1     10 = 2•5

(10)¹¹ = (2•5)¹¹ = 2¹¹ • 5¹¹

Equation at the end of step  4  :

   781
  (——— • (211•511)) • (512•210)
   100

Step  5  :

            781
 Simplify   ———
            100

Equation at the end of step  5  :

   781
  (——— • (211•511)) • (512•210)
   100

Step  6  :

Dividing exponents :

 6.1    2¹¹   divided by   2²   = 2^{(11 - 2)} = 2⁹

Dividing exponents :

 6.2    5¹¹   divided by   5²   = 5^{(11 - 2)} = 5⁹

Equation at the end of step  6  :

  (11•71•29•59) • (512•210)

Step  7  :

Multiplying exponents :

 7.1    2⁹  multiplied by  2¹⁰   = 2^{(9 + 10)} = 2¹⁹

Multiplying exponents :

 7.2    5⁹  multiplied by  5¹²   = 5^{(9 + 12)} = 5²¹

Final result :

  (11•71•219•521)