5.1 Roots and rational exponents

Ideas in this lesson

Even roots

An even root has a nonnegative principal value. Over the reals, its radicand must be nonnegative.

Odd roots

An odd root preserves the sign of its radicand; negative inputs have negative real odd roots.

Rewrite radicals and rational powers

For a positive base, the denominator of a reduced rational exponent is the root index and the numerator is the power.

Evaluate rational powers

Find the indicated root, then raise it to the numerator power. Respect the real domain before evaluating.