Simplify the surd below. Write your answer with a fractional exponent. 40‾‾‾√3

To simplify the surd $\sqrt[3]{40}$ and express it with a fractional exponent, follow these steps:

1. Break Down the Problem

   The problem requires expressing the cube root of 40 using a fractional exponent. The cube root of a number $x$ can be expressed as $x^{1/3}$.

2. Relevant Concepts

   The cube root of a number $x$ is equivalent to raising that number to the power of $1/3$. Therefore, $\sqrt[3]{x} = x^{1/3}$.

3. Analysis and Detail

   For the given surd $\sqrt[3]{40}$, we can directly apply the concept of fractional exponents: $\sqrt[3]{40} = 40^{1/3}$

4. Verify and Summarize

   Verify that the expression $40^{1/3}$ correctly represents the cube root of 40. This is a standard representation in mathematics for expressing roots using exponents.

Final Answer

The simplified form of the surd $\sqrt[3]{40}$ with a fractional exponent is $40^{1/3}$.