Fractional exponents link roots and powers.
About this calculator
Fractional exponents link roots and powers. b^(2/3) means cube root of b, then square the result — or equivalently take the cube root of b squared. For 8^(2/3): ∛8 = 2, then 2² = 4.
Even denominators like 1/2 or 3/4 require a non-negative base in the real numbers. Odd denominators like 1/3 accept negatives: (−8)^(1/3) = −2.
Connects to [[square-root]] and [[cube-root]] as special cases. For solving the exponent when you know base and result, use [[solve-for-exponent]]. General integer powers live in [[exponent]].
Common uses
- Evaluate 8^(2/3) in algebra homework
- Convert √(x³) to x^(3/2) notation
- Check rational exponent rules before a test
- Compute compound root-and-power expressions
- Verify calculator results for fractional powers
Frequently asked questions
What is 8 raised to the 2/3 power?
8^(2/3) = (∛8)² = 2² = 4. You can also compute ∛(8²) = ∛64 = 4.
Why must the base be non-negative for even denominators?
Even roots of negatives are not real. 4^(1/2) = √4 = 2 works, but (−4)^(1/2) has no real answer.
How does b^(1/2) relate to square roots?
b^(1/2) = √b exactly. Fractional exponents are just another way to write roots.
What is 27^(1/3)?
27^(1/3) = ∛27 = 3. A denominator of 1 means a whole-number exponent with no root.