if a is a rational number and n is positive integer greater than 1 .prove that a^n is rational

Hello student,
Please find the answer to your question
Given a is a rational number so it can be expressed as p/q
where p,q are some integers and q>0
as n>1 and is a positive integer
if n=2 thena²=(p/q)²=(p*p)/(q*q)=rational (since product of two rational numbers is rational and also p/q is rational)
similarly for n=3,4,......N by the principle of mathematical induction
aⁿis rational for all n>1 and n=postive integer