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 \(\sqrt[3]{216}\) using rational exponents, we can write it in the following way:

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

In this case, \(216\) is raised to the power of \(1/3\), which indicates that the expression is equivalent to the cube root of \(216\).

Thus, the rational exponent on the expression equivalent to \(\sqrt[3]{216}\) is:

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

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

just choose a, b, c, or d

The correct choice is **b (1/3)**.