Question

express $18^{\frac{1}{4}}$ in simplest radical form.

Explanation:

Step1: Recall the exponent rule

Recall that \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\), so \(18^{\frac{1}{4}}=\sqrt[4]{18}\).

Step2: Factor the radicand

Factor \(18 = 2\times9=2\times3^2\), so \(\sqrt[4]{18}=\sqrt[4]{2\times3^2}\).
Since there are no perfect fourth - power factors in \(18\) (the perfect fourth - powers are \(1, 16, 81,\cdots\) and \(18\) is not divisible by \(16\) or other perfect fourth - powers), the simplest radical form of \(18^{\frac{1}{4}}\) is \(\sqrt[4]{18}\).

Answer:

\(\sqrt[4]{18}\)