Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-2" was replaced by "^(-2)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (106) +  ((2)(-2)•(5)(-2))

Step  2  :

 2.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  2  :

  (26•56) +  ((2)(-2)•(5)(-2))

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2² • 5²  as the denominator :

               (26•56)     (26•56) • (22•52)
    (26•56) =  ———————  =  —————————————————
                  1             (22•52)     

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 :

 3.2       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 :

 2⁶  multiplied by  2²   = 2^{(6 + 2)} = 2⁸

Multiplying exponents :

 5⁶  multiplied by  5²   = 5^{(6 + 2)} = 5⁸ (2⁶•5⁶) • 100 + 1 2⁸•5⁸ + 1 ————————————————— = ————————— 100 100

Final result :

  10 + 1
  ——————
   100