Solution - Reducing fractions to their lowest terms

Step  1  :

             647
 Simplify   ————
            2020

Equation at the end of step  1  :

                 647
  ((a4) • a) +  ————
                2020
 Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  2020  as the denominator :

           a5     a5 • 2020
     a5 =  ——  =  —————————
           1        2020   

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:

 a5 • 2020 + 647     2020a5 + 647
 ———————————————  =  ————————————
      2020               2020    

Polynomial Roots Calculator :

 2.3    Find roots (zeroes) of :       F(a) = 2020a⁵ + 647
Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2020  and the Trailing Constant is  647.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,4 ,5 ,10 ,20 ,101 ,202 ,404 ,505 , etc
 of the Trailing Constant :  1 ,647

 Let us test ....

Note - For tidiness, printing of 35 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Final result :

  2020a5 + 647
  ————————————
      2020