Solution - Power equations

Step  1  :

 1.1     25 = 52

(25)¹ = (5²)¹ = 5²

Equation at the end of step  1  :

   (42)           52
  (————+(7•(23)))-——
    2             2 

Step  2  :

            52
 Simplify   ——
            2 

Equation at the end of step  2  :

   (42)           25
  (————+(7•(23)))-——
    2             2 

Step  3  :

Equation at the end of step  3  :

   (42)                 25
  (———— +  (7 • 23)) -  ——
    2                   2 

Step  4  :

Equation at the end of step  4  :

   (42)               25
  (———— +  (7•23)) -  ——
    2                 2 

Step  5  :

 5.1     4 = 22

(4)² = (2²)² = 2⁴

Equation at the end of step  5  :

   24               25
  (—— +  (7•23)) -  ——
   2                2 

Step  6  :

            24
 Simplify   ——
            2 

Dividing exponents :

 6.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Equation at the end of step  6  :

                   25
  (8 +  (7•23)) -  ——
                   2 

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

           64     64 • 2
     64 =  ——  =  ——————
           1        2   

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:

 64 • 2 - (25)     103
 —————————————  =  ———
       2            2 

Final result :

  103            
  ——— = 51.50000 
   2