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.