Prove or disprove that if a and b are rational numbers then a^b is also rational

Solution:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Every integer is a rational number.

We have to prove or disprove that if a and b are rational numbers then ab is also rational

Assume a = 3 and b = 2

a^b = 3² = 9 which is a rational number

So the statement is true.

Assume a = 5 and b = 1/2

ab = 5^1/2 = √5 which is not rational

So the statement is false.

Therefore, ab can be rational or irrational.

Prove or disprove that if a and b are rational numbers then ab is also rational

Summary:

If a and b are rational numbers then a^b can be rational or irrational.