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
Start Fraction 1 over 3 End Fraction

3
3

−3
negative 3

−13
negative Start Fraction 1 over 3 End Fraction

Answer 1

To find the rational exponent equivalent to \( \sqrt[3]{216} \), we can rewrite it using the properties of exponents.

The cube root can be expressed as an exponent of \( \frac{1}{3} \):
\[
\sqrt[3]{216} = 216^{\frac{1}{3}}
\]

Now, to relate \( 216^{\frac{1}{3}} \) to the expression \( 216^{-\frac{1}{3}} \), we note that in the original question you have \( \sqrt[3]{216}^3 \) (if that's what it means by 216 raised to the power of "negative 3"). But if we consider only \( 216^{\frac{1}{3}} \), it remains as above:

To summarize, the rational exponent on an expression equivalent to \( \sqrt[3]{216} \) is:
\[
\frac{1}{3}
\]

Thus, the correct response is:
**Start Fraction 1 over 3 End Fraction**