Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.7" was replaced by "(37/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  1  :

   28          37
  (——•(1010))•(——•(28•58))
   10          10

Step  2  :

            37
 Simplify   ——
            10

Equation at the end of step  2  :

   28              37
  (—— • (1010)) • (—— • (28•58))
   10              10

Step  3  :

Dividing exponents :

 3.1    2⁸   divided by   2¹   = 2^{(8 - 1)} = 2⁷

Raising to a Power :

 3.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  3  :

   28
  (—— • (1010)) • (37•27•57)
   10

Step  4  :

 4.1     10 = 2•5

(10)¹⁰ = (2•5)¹⁰ = 2¹⁰ • 5¹⁰

Equation at the end of step  4  :

   28
  (—— • (210•510)) • (37•27•57)
   10

Step  5  :

            14
 Simplify   ——
            5 

Equation at the end of step  5  :

   14
  (—— • (210•510)) • (37•27•57)
   5 

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2¹⁰   = 2^{(1 + 10)} = 2¹¹

Dividing exponents :

 6.2    5¹⁰   divided by   5¹   = 5^{(10 - 1)} = 5⁹

Equation at the end of step  6  :

  (211•7•59) • (37•27•57)

Step  7  :

Multiplying exponents :

 7.1    2¹¹  multiplied by  2⁷   = 2^{(11 + 7)} = 2¹⁸

Multiplying exponents :

 7.2    5⁹  multiplied by  5⁷   = 5^{(9 + 7)} = 5¹⁶

Final result :

  (218•7•516•37)