using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to \root(3)(216)

To express \(\root{3}{216}\) using rational exponents, we start by recognizing that the cube root can be represented as an exponent:

\[
\root{3}{216} = 216^{1/3}
\]

The expression \(216^{1/3}\) indicates that we are taking the third root of 216, which corresponds to raising 216 to the power of \(1/3\).

Now, regarding the options provided:

- \(-3\)
- \(1/3\)
- \(3\)
- \(-1/3\)

The correct rational exponent corresponding to \(\root{3}{216}\) is:

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

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

just choose a,b,c, or d

The correct answer is **b. \( \frac{1}{3} \)**.