Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to 216−−−√3 ?(1 point)Responses−13negative Start Fraction 1 over 3 End Fraction13Start Fraction 1 over 3 End Fraction−3negative 33

Answer 1

To simplify the expression \( \sqrt[3]{216} \) using rational exponents, we start by rewriting the expression:

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

Now, if we have \( 216^{1/3} \), we can analyze the exponent part:

• Since \( \sqrt[3]{216} \) means taking the cube root of 216, this is equivalent to raising 216 to the power of \( \frac{1}{3} \).

Therefore, the expression \( \sqrt[3]{216} \) represented as a rational exponent is:

\[ 216^{1/3} \]

The options provided in your question include negative exponents and fractions. Among the options given, the correct equivalent expression for the rational exponent on the expression \( \sqrt[3]{216} \) is:

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

Thus, the answer is:

Start Fraction 1 over 3 End Fraction.