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)

Question

Responses

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

1/3
Start Fraction 1 over 3 End Fraction

3
3

−3

Answer 1

To generate an equivalent expression using rational exponents for \( \sqrt[3]{216} \), we can rewrite the expression in terms of rational exponents.

The cube root of a number can be represented as raising that number to the power of \( \frac{1}{3} \). Therefore:

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

Now, we need to consider the original expression \( 216^{−1/3} \). This expression indicates that we are taking the cube root of 216 and then taking the reciprocal (due to the negative exponent).

Thus, the rational exponent on the equivalent expression for \( 216^{−1/3} \) is:

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

So, the correct response is:

−1/3