Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

Step  1  :

 1.1     4 = 22

(4)^-3 = (2²)^(-3) = (2)^(-6)

Equation at the end of step  1  :

  ((4-2) +  (2)(-6)) +  1

Step  2  :

 2.1     4 = 22

(4)^-2 = (2²)^(-2) = (2)^(-4)

Equation at the end of step  2  :

  ((2)(-4) +  (2)(-6)) +  1

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       16 

      The right denominator is :       64 

      Least Common Multiple:
      64 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 4

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      4
   ——————————————————  =  ——
         L.C.M            64

   R. Mult. • R. Num.       1
   ——————————————————  =   ——
         L.C.M             64

Adding fractions that have a common denominator :

 3.4       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:

 4 + 1      5
 —————  =  ——
  64       64

Equation at the end of step  3  :

   5    
  —— +  1
  64    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  64  as the denominator :

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

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

 5 + 64     69
 ——————  =  ——
   64       64

Final result :

  69           
  —— = 1.07812 
  64