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)

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Responses

Answer 1

To convert the expression \( 216^{-\frac{1}{3}} \) into a form with a rational exponent, we can apply the properties of exponents.

The expression \( 216^{-\frac{1}{3}} \) means:

1. The negative exponent indicates that we take the reciprocal of the base: \[ 216^{-\frac{1}{3}} = \frac{1}{216^{\frac{1}{3}}} \]

2. The exponent of \( \frac{1}{3} \) indicates that we take the cube root of 216.

Thus, the expression \( 216^{-\frac{1}{3}} \) is equivalent to: \[ \frac{1}{\sqrt[3]{216}} \]

In terms of a rational exponent, it is represented as: \[ 216^{-\frac{1}{3}} \]

Therefore, the rational exponent for the expression \( 216^{-\frac{1}{3}} \) is \( -\frac{1}{3} \).