Radicals & Rational Exponents Quick Check

Question

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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

3
3

−3
negative 3

13
Start Fraction 1 over 3 End Fraction

−13
negative Start Fraction 1 over 3 End Fraction
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Answer 1

To convert the expression \( \sqrt[3]{216} \) into an equivalent expression using rational exponents, we can use the property that \( \sqrt[n]{a} = a^{\frac{1}{n}} \).

In this case, we have:

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

So, the rational exponent on the expression equivalent to \( \sqrt[3]{216} \) is \( \frac{1}{3} \).

The correct response is:

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