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
3

13
Start Fraction 1 over 3 End Fraction

−3
negative 3

−13

GPT-4o mini · Answer

To convert the expression $ 216^{\frac{1}{3}} $ to its equivalent form using rational exponents, we can apply the property of exponents that states that $ a^{\frac{m}{n}} $ is equal to the $ n $-th root of $ a $ raised to the power of $ m $. In this case, $ 216^{\frac{1}{3}} $ means the cube root of 216. So, the rational exponent corresponding to $ 216^{\frac{1}{3}} $ is $ \frac{1}{3} $. Thus, the correct response is: **Start Fraction 1 over 3 End Fraction** (or $\frac{1}{3}$).