If a is a positive rational number and n is a positive integer greater than 1, prove that aⁿ is a rational number.

Rational Number is a number that can be expressed in the form p/q, where q not equal to zero.

Let there be two rational numbers x and y

There product will be equal to xy, and also will be in p/q form

Product of two rational number is always a rational number.

Hence if a is a rational number, then

a² = a x a is a rational number,

a³ = a² x a is a rational number.

.^.. aⁿ = a x a x a x a...... to n times is a rational number.