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

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