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

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

−3
negative 3

13
Start Fraction 1 over 3 End Fraction

3
3

−13

GPT-4o mini · Answer

To convert the expression $ \sqrt[3]{216} $ to an expression with a rational exponent, we can express the cube root of 216 as follows: $$ \sqrt[3]{216} = 216^{\frac{1}{3}} $$ Therefore, if we have $ 216^{\frac{1}{3}} $, this is the same as saying: $$ 216^{-\frac{3}{3}} = 216^{-1} $$ However, since the problem is specifically exploring the exponent on $ 216^{\frac{1}{3}} $, the rational exponent associated with $ \sqrt[3]{216} $ is $ \frac{1}{3} $, not any negative exponent. Thus, the correct response for the rational exponent is: **Start Fraction 1 over 3 End Fraction** So the answer is $ \frac{1}{3} $.