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

Question

?(1 point)
Responses

−3
negative 3

3
3

13
Start Fraction 1 over 3 End Fraction

−13

Answer 1

To express \( 216^{-\frac{1}{3}} \) in terms of rational exponents, we can utilize the properties of exponents.

The expression \( 216^{-\frac{1}{3}} \) indicates taking the cube root of 216 and then applying the negative exponent, which suggests that the result will be in the denominator.

1. First, we convert the cube root into a rational exponent: \[ 216^{-\frac{1}{3}} = \frac{1}{216^{\frac{1}{3}}} \]

The rational exponent of the expression \( 216^{-\frac{1}{3}} \) is therefore \( -\frac{1}{3} \).

From the options provided, the equivalent expression therefore corresponds to the following:

• Response: \(-\frac{1}{3}\)