Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "3.5" was replaced by "(35/10)". 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  :

   125          35
  (———•(10-5))•(——•(25•55))
   100          10

Step  2  :

            7
 Simplify   —
            2

Equation at the end of step  2  :

   125              7
  (——— • (10-5)) • (— • (25•55))
   100              2

Step  3  :

Raising to a Power :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Equation at the end of step  3  :

   125
  (——— • (10-5)) • (7•24•55)
   100

Step  4  :

 4.1     10 = 2•5

(10)^-5 = (2•5)^(-5) = (2)^(-5) • (5)^(-5)

Equation at the end of step  4  :

   125
  (——— • ((2)(-5)•(5)(-5))) • (7•24•55)
   100

Step  5  :

            5
 Simplify   —
            4

Equation at the end of step  5  :

   5
  (— • ((2)(-5)•(5)(-5))) • (7•24•55)
   4

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Dividing exponents :

 6.2    5¹   divided by   5⁵   = 5^{(1 - 5)} = 5^(-4) = ¹/_5⁴

Equation at the end of step  6  :

     1   
  ——————— • (7•24•55)
  (27•54)

Step  7  :

Dividing exponents :

 7.1    2⁴   divided by   2⁷   = 2^{(4 - 7)} = 2^(-3) = ¹/_2³

Dividing exponents :

 7.2    5⁵   divided by   5⁴   = 5^{(5 - 4)} = 5¹ = 5

Final result :

  35           
  —— = 4.37500 
  8