Rational exponents

Math

Definition

Exponents that are fractions, where the numerator indicates the power and the denominator indicates the root. They provide an alternative notation for radicals.

Examples

  • 8^(2/3) = (∛8)² = 2² = 4
  • x^(1/2) = √x
  • 27^(-1/3) = 1/∛27 = 1/3
Key Fact

x^(m/n) = ⁿ√(xᵐ) = (ⁿ√x)ᵐ

Related Terms

Nth roots Exponent rules Operations with radicals Simplifying radicals

Study This Concept

Practice rational exponents with free review games in these units:

Algebra 2 Unit 6: Radical Functions