Solution - Power equations

Step  1  :

Equation at the end of step  1  :

     32           
  (————— +  7) -  22
   (164)          

Step  2  :

 2.1     16 = 24

(16)⁴ = (2⁴)⁴ = 2¹⁶

Equation at the end of step  2  :

    32          
  (——— +  7) -  22
   216          

Step  3  :

             32
 Simplify   ———
            216

Dividing exponents :

 3.1    2⁵   divided by   2¹⁶   = 2^{(5 - 16)} = 2^(-11) = ¹/_2¹¹

Equation at the end of step  3  :

     1           
  (———— +  7) -  22
   2048          

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2048  as the denominator :

         7     7 • 2048
    7 =  —  =  ————————
         1       2048  

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:

 1 + 7 • 2048     14337
 ————————————  =  —————
     2048         2048 

Equation at the end of step  4  :

  14337    
  ————— -  22
  2048     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2048  as the denominator :

          22     22 • 2048
    22 =  ——  =  —————————
          1        2048   

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 14337 - (22 • 2048)     6145
 ———————————————————  =  ————
        2048             2048

Final result :

  6145           
  ———— = 3.00049 
  2048