Radicals and Rational Exponents

Overview

Goal. Rewrite radicals as powers with fractional exponents and back, and evaluate fractional powers of perfect powers.

Rational exponent (definition). An exponent written as a fraction: the denominator names a root, and the numerator is an ordinary power.

Fractional exponents are roots: converting and evaluating both ways.

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Goal. Move both ways between radical form and rational-exponent form, and evaluate powers whose exponents are fractions.

Rational exponent (definition). An exponent written as a fraction: the denominator names a root, and the numerator is an ordinary power.