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)

(2): "1.6" was replaced by "(16/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

                   16
  (5 • (10-2)) +  (—— • ((2)(-3)•(5)(-3)))
                   10

Step  2  :

            8
 Simplify   —
            5

Equation at the end of step  2  :

                   8
  (5 • (10-2)) +  (— • ((2)(-3)•(5)(-3)))
                   5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Raising to a Power :

 3.2      Canceling out  2³ as it appears on both sides of the fraction line

Equation at the end of step  3  :

                   1 
  (5 • (10-2)) +  ———
                  625

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

                              1 
  (5 • ((2)(-2)•(5)(-2))) +  ———
                             625

Step  5  :

Dividing exponents :

 5.1    5¹   divided by   5²   = 5^{(1 - 2)} = 5^(-1) = ¹/_5¹ = ¹/₅

Equation at the end of step  5  :

   1     1 
  —— +  ———
  20    625

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       625 

      Least Common Multiple:
      2500 

Calculating Multipliers :

 6.2    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 = 125

   Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

 6.3      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.       125
   ——————————————————  =   ————
         L.C.M             2500

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

Adding fractions that have a common denominator :

 6.4       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:

 125 + 4      129
 ———————  =  ————
  2500       2500

Final result :

   129           
  ———— = 0.05160 
  2500