Radicals & Rational Exponents Quick Check

1 of 51 of 5 Items
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

13
Start Fraction 1 over 3 End Fraction

−13
negative Start Fraction 1 over 3 End Fraction

−3
negative 3

3

1 answer

To convert the expression \( \sqrt[3]{216} \) to using rational exponents, we can express it as:

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

Thus, the rational exponent on the expression equivalent to \( \sqrt[3]{216} \) is:

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

From the options you provided, the correct response is:

Start Fraction 1 over 3 End Fraction (which as a fraction is \( \frac{1}{3} \)).