Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.7" was replaced by "(47/10)". 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  :

   13       47
  (——•(107))——•(25•55))
   10(      10

Step  2  :

            47
 Simplify   ——
            10

Equation at the end of step  2  :

   13             47
  (—— • (107)) ÷ (—— • (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  :

   13
  (—— • (107)) ÷ (47•24•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   13
  (—— • (27•57)) ÷ (47•24•54)
   10

Step  5  :

            13
 Simplify   ——
            10

Equation at the end of step  5  :

  13
  —— • (27•57)) ÷ (47•24•54)
  10

Step  6  :

Dividing exponents :

 6.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Dividing exponents :

 6.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  6  :

Step  7  :

            (13•26•56)
 Simplify   ——————————
            (47•24•54)

Dividing exponents :

 7.1    2⁶   divided by   2⁴   = 2^{(6 - 4)} = 2²

Dividing exponents :

 7.2    5⁶   divided by   5⁴   = 5^{(6 - 4)} = 5²

Final result :

  1300            
  ———— = 27.65957 
   47