Rational Exponents Calculator

Math

Calculate powers with fractional exponents. Formula: base^(m/n) = ⁿ√(base^m). Example: 8^(2/3) = ³√(8²) = 4.

Formula

base^(m/n) = ⁿ√(base^m)
  • Rational exponents combine powers and roots
  • a^(m/n) = (ⁿ√a)^m = ⁿ√(a^m)
  • m = numerator (power), n = denominator (root index)
  • Example: 27^(2/3) = ³√(27²) = ³√729 = 9
  • Base must be ≥ 0 for real numbers

Example

Inputs
  • Base: 8
  • Numerator (m): 2
  • Denominator (n): 3

8^(2/3) = ³√(8²) = ³√64 = 4

Frequently asked questions

What does 8^(2/3) mean?
Cube root of 8 squared: (³√8)² = 2² = 4
Can I use negative bases?
Only if n is odd. Negative base with even root = no real result.