Use the Negative Exponent Rule to generate an equivalent expression to [tex]3^{\frac{-1}{2}}[/tex].

[tex]\square[/tex]

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Answer :

To generate an equivalent expression for [tex]\( 3^{\frac{-1}{2}} \)[/tex] using the Negative Exponent Rule, follow these steps:

1. Understand the Negative Exponent Rule: The rule states that [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]. This means that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent.

2. Apply the Rule: For the given expression [tex]\( 3^{\frac{-1}{2}} \)[/tex]:
[tex]\[ 3^{\frac{-1}{2}} = \frac{1}{3^{\frac{1}{2}}} \][/tex]

3. Simplify the Expression: Recognize that [tex]\( 3^{\frac{1}{2}} \)[/tex] represents the square root of 3:
[tex]\[ 3^{\frac{1}{2}} = \sqrt{3} \][/tex]

4. Combine the Steps: Substitute back into the equation:
[tex]\[ 3^{\frac{-1}{2}} = \frac{1}{\sqrt{3}} \][/tex]

The equivalent expression using the Negative Exponent Rule is [tex]\( \frac{1}{\sqrt{3}} \)[/tex].

Evaluating this expression, we find that the numerical result is approximately [tex]\( 0.5773502691896258 \)[/tex].