3 answers
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To express \(\root{3}{216}\) using rational exponents, we start by recognizing that the cube root can be represented as an exponent:
\[
\root{3}{216} = 216^{1/3}
\]
The expression \(216^{1/3}\) indicates that we are taking the third root of 216, which corresponds to raising 216 to the power of \(1/3\).
Now, regarding the options provided:
- \(-3\)
- \(1/3\)
- \(3\)
- \(-1/3\)
The correct rational exponent corresponding to \(\root{3}{216}\) is:
\[
\frac{1}{3}
\]
So, the answer is \( \frac{1}{3} \).