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

−3
negative 3

−13
negative Start Fraction 1 over 3 End Fraction

13
Start Fraction 1 over 3 End Fraction

3

Answer 1

To express \( 216^{-\frac{1}{3}} \) using rational exponents, we first note that \( 216^{-\frac{1}{3}} \) can be written as:

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

The expression \( 216^{\frac{1}{3}} \) denotes the cube root of 216. Therefore, the expression \( 216^{-\frac{1}{3}} \) represents the reciprocal of the cube root of 216.

Thus, the rational exponent in the expression \( 216^{-\frac{1}{3}} \) is \( -\frac{1}{3} \).

So the correct answer is:

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