Question

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 −13 negative Start Fraction 1 over 3 End Fraction 13 Start Fraction 1 over 3 End Fraction 3 3 −3 negative 3

Answer 1

To rewrite \( \sqrt[3]{216} \) using rational exponents, we first express the cube root in exponent form. The cube root of a number can be written as raising the number to the power of \( \frac{1}{3} \).

Thus, we have:

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

The question refers to \( 216^{\frac{1}{3}} \). Therefore, the property of exponents being used here indicates that the rational exponent for \( \sqrt[3]{216} \) is:

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

So the answer to your question is:

Start Fraction 1 over 3 End Fraction (or \( \frac{1}{3} \)).