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 \( \frac{1}{3} \).