Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "5.8" was replaced by "(58/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-1 = (2•5)^(-1) = (2)^(-1) • (5)^(-1)

Equation at the end of step  1  :

   636         58
  (———•(103))-(——•((2)(-1)•(5)(-1)))
   100         10

Step  2  :

            29
 Simplify   ——
            5 

Equation at the end of step  2  :

   636              29
  (——— • (103)) -  (—— • ((2)(-1)•(5)(-1)))
   100              5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5¹   = 5^{(1 + 1)} = 5²

Equation at the end of step  3  :

   636             29
  (——— • (103)) -  ——
   100             50

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   636               29
  (——— • (23•53)) -  ——
   100               50

Step  5  :

            159
 Simplify   ———
            25 

Equation at the end of step  5  :

   159               29
  (——— • (23•53)) -  ——
   25                50

Step  6  :

Dividing exponents :

 6.1    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  6  :

          29
  6360 -  ——
          50

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  50  as the denominator :

             6360     6360 • 50
     6360 =  ————  =  —————————
              1          50    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 7.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 6360 • 50 - (29)     317971
 ————————————————  =  ——————
        50              50  

Final result :

  317971              
  —————— = 6359.42000 
    50