Understanding Rational Exponents

Front

Rational Exponent

Back

An exponent that is a fraction

Front

a^{m/n}

Back

\sqrt[n]{a^m}

Front

8^{2/3}

Back

\sqrt[3]{8^2} = \sqrt[3]{64} = 4

Front

a^{1/n}

Back

\sqrt[n]{a}

Front

(a^{m/n})^p

Back

a^{m \cdot p/n}

Front

a^{m/n} \cdot a^{p/q}

Back

a^{(mq + np)/(nq)}

Front

(a/b)^{m/n}

Back

a^{m/n}/b^{m/n}

Front

\sqrt[4]{16}

Back

16^{1/4} = 2

Front

27^{2/3}

Back

\sqrt[3]{27^2} = \sqrt[3]{729} = 9

Front

(16^{1/2})^2

Back

16^{1/2 \cdot 2} = 16^1 = 16