Question

Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to exponent 3 root 216?

Answer 1

To express the cube root of 216 using rational exponents, we can use the property that states:

\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\]

In our case, we need to find the cube root of 216, which is expressed as:

\[
\sqrt[3]{216} = 216^{\frac{1}{3}}
\]

Thus, the rational exponent on an expression equivalent to the cube root of 216 is:

\[
\frac{1}{3}
\]

So the answer is \( \frac{1}{3} \).