Question

question
express $18^{\frac{1}{4}}$ in simplest radical form.
answer attempt 1 out of 2

Explanation:

Step1: Recall the exponent rule

The rule for converting a fractional exponent to a radical is $a^{\frac{m}{n}}=\sqrt[n]{a^m}$. For $18^{\frac{1}{4}}$, we have $m = 1$ and $n=4$, so $18^{\frac{1}{4}}=\sqrt[4]{18}$.

Step2: Simplify the radical (if possible)

Factor 18: $18 = 2\times3^2$. Since there are no perfect fourth - power factors in 18 (a perfect fourth - power is a number of the form $k^4$ where $k$ is an integer, e.g., $1^4 = 1$, $2^4=16$, $3^4 = 81$ and 18 is between $2^4$ and $3^4$ and its factors don't include a perfect fourth - power other than 1), $\sqrt[4]{18}$ is already in simplest radical form.

Answer:

$\sqrt[4]{18}$