Express 48, start superscript, one quarter, end superscript48 41​ in simplest radical form.

To express $48^{\frac{1}{4}}$ in simplest radical form, we can follow these steps:

1. ### Break Down the Problem

We need to simplify the expression $48^{\frac{1}{4}}$.

2. ### Relevant Concepts

The expression $a^{\frac{m}{n}}$ can be represented as $\sqrt[n]{a^m}$. Therefore, $48^{\frac{1}{4}}$ can be rewritten as $\sqrt[4]{48}$.

3. ### Analysis and Detail

Now, we need to simplify $\sqrt[4]{48}$.

1. Factor 48 into its prime factors: $48 = 16 \times 3 = 2^4 \times 3^1$

2. Substituting back into the radical: $48^{\frac{1}{4}} = (2^4 \times 3^1)^{\frac{1}{4}} = 2^{\frac{4}{4}} \times 3^{\frac{1}{4}} = 2^1 \times 3^{\frac{1}{4}}$

3. Simplifying further: $2 \times \sqrt[4]{3}$

4. ### Verify and Summarize

The expression $48^{\frac{1}{4}}$ simplifies to $2 \sqrt[4]{3}$.

Final Answer

The simplest radical form of $48^{\frac{1}{4}}$ is $2 \sqrt[4]{3}$.