What is rational powers?

Answer 1

Rational powers refer to expressions of the form (x^{\frac{m}{n}}), where (x) is a base, (m) and (n) are integers, and (n) is a positive integer. This expression can be interpreted as taking the (n)-th root of (x^m), or equivalently, raising (x) to the (m)-th power and then taking the (n)-th root. For example, (x^{\frac{1}{2}}) represents the square root of (x), while (x^{\frac{3}{2}}) represents the square root of (x) cubed. Rational powers are commonly used in algebra and calculus to simplify expressions and solve equations.