Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-12" was replaced by "^(-12)".

(2): "0.0125" was replaced by "(0125/10000)".

Step  1  :

             1
 Simplify   ——
            80

Equation at the end of step  1  :

          1
  ((1 +  ——)-12) • 20
         80

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  80  as the denominator :

          1     1 • 80
     1 =  —  =  ——————
          1       80  

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 :

 2.2       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:

 80 + 1     81
 ——————  =  ——
   80       80

Equation at the end of step  2  :

   81
  (——)-12) • 20
   80

Step  3  :

 3.1     81 = 34

(81)^-12 = (3⁴)^(-12) = (3)^(-48)  3.2     80 = 2⁴•5 (80)^-12 = (2⁴•5)^(-12) = (2)^(-48) • (5)^(-12)

Equation at the end of step  3  :

        (3)(-48)     
  ——————————————————— • 20
  ((2)(-48)•(5)(-12)) 

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁴⁸   = 2^{(2 + 48)} = 2⁵⁰

Multiplying exponents :

 4.2    5¹  multiplied by  5¹²   = 5^{(1 + 12)} = 5¹³

Final result :

  (250•513)            
  ————————— = 17.23017 
     348