Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  1  :

  (8 • (10-4)) +  (1 • ((2)(-6)•(5)(-6)))

Step  2  :

 2.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  2  :

                                1   
  (8 • ((2)(-4)•(5)(-4))) +  ———————
                             (26•56)

Step  3  :

Dividing exponents :

 3.1    2³   divided by   2⁴   = 2^{(3 - 4)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  3  :

    1        1   
  ———— +  ———————
  1250    (26•56)

Step  4  :

 4.1      Finding a Common Denominator   The left  1250 
 The right  26 • 56 

 The product of any two denominators can be used
 as a common denominator. 

 Said product is not necessarily the least common 
 denominator.

 As a matter of fact, whenever the two denominators
have a common factor, their product will be bigger
 than the least common denominator. 

Anyway, the product is a fine common denominator and
 can perfectly be used for 
 calculating multipliers, as well as for generating
 equivalent fractions. 

 1250 • 26 • 56   will be used as a common denominator.

Calculating Multipliers :

 4.2    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 = 2⁶ • 5⁶

   Right_M = L.C.M / R_Deno = 1250

Making Equivalent Fractions :

 4.3      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.                      (26•56)   
   ——————————————————  =               ——————————————
             Common denominator        1250 • (26•56)

   R. Mult. • R. Num.                       1250     
   ——————————————————  =               ——————————————
             Common denominator        1250 • (26•56)

Adding fractions that have a common denominator :

 4.4       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:

 (26•56) + 1250      26•56 + 1250 
 ——————————————  =  ——————————————
 1250 • (26•56)     1250 • (26•56)

Final result :

     1 + 1250   
  ——————————————
  1250 • (26•56)