Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.314" was replaced by "(2314/1000)".

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   2314                
  (———— • (22•52)) -  8
   1000                

Step  2  :

            1157
 Simplify   ————
            500 

Equation at the end of step  2  :

   1157                
  (———— • (22•52)) -  8
   500                 

Step  3  :

Canceling Out :

 3.1      Canceling out  2² as it appears on both sides of the fraction line

Dividing exponents :

 3.2    5²   divided by   5³   = 5^{(2 - 3)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  3  :

  1157    
  ———— -  8
   5      

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

         8     8 • 5
    8 =  —  =  —————
         1       5  

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 :

 4.2       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:

 1157 - (8 • 5)     1117
 ——————————————  =  ————
       5             5  

Final result :

  1117             
  ———— = 223.40000 
   5