# Prove or disprove that if a and b are rational numbers, then a^{b} is rational

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.

## Answer: It can be rational or irrational

Prove/ disprove that if a and b are rational, then a^{b} is rational

**Explanation:**

Let a=2 and b=4

a^{b} = 2^{4} = 16, which is a rational number.

### Therefore, the statement is true.

Let a = 2 and b = 1/2

a^{b}= 2^{1/2} = **√**2 which is not a rational number