Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (100 • (10-4)) +  (32 • ((2)(-4)•(5)(-4)))

Step  2  :

Raising to a Power :

 2.1    2⁵   divided by   2⁴   = 2^{(5 - 4)} = 2¹ = 2

Equation at the end of step  2  :

                     2 
  (100 • (10-4)) +  ———
                    625

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

                                2 
  (100 • ((2)(-4)•(5)(-4))) +  ———
                               625

Step  4  :

Dividing exponents :

 4.1    2²   divided by   2⁴   = 2^{(2 - 4)} = 2^(-2) = ¹/_2²

Dividing exponents :

 4.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Equation at the end of step  4  :

   1      2 
  ——— +  ———
  100    625

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       100 

      The right denominator is :       625 

      Least Common Multiple:
      2500 

Calculating Multipliers :

 5.2    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 = 25

   Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

 5.3      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.       25 
   ——————————————————  =   ————
         L.C.M             2500

   R. Mult. • R. Num.      2 • 4
   ——————————————————  =   —————
         L.C.M             2500 

Adding fractions that have a common denominator :

 5.4       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:

 25 + 2 • 4      33 
 ——————————  =  ————
    2500        2500

Final result :

   33            
  ———— = 0.01320 
  2500