Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)".

Step  1  :

 1.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  1  :

  720 -  ((2)(-9)•(5)(-9))

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2⁹ • 5⁹  as the denominator :

           720     720 • (29•59)
    720 =  ———  =  —————————————
            1         (29•59)   

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

Calculating Multipliers :

 2.2    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 = 2⁹ • 5⁹

   Right_M = L.C.M / R_Deno = 1

Adding fractions that have a common denominator :

 2.3       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:

Multiplying exponents :

 2⁴  multiplied by  2⁹   = 2^{(4 + 9)} = 2¹³

Multiplying exponents :

 5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰ 720 • (2⁹•5⁹) - (1) 2¹³•3²•5¹⁰ - 1 ——————————————————— = —————————————— (2⁹•5⁹) 1

Final result :

  720 - 1
  ———————
     1