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Radicals & Rational Exponents Quick Check

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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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

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