Use the negative exponent rule to generate an equivalent expression to 3 and Negative one half

Answer 1

The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \). To apply this rule to the expression \( 3^{-1/2} \), we proceed as follows:

1. Rewrite the expression using the negative exponent rule: \[ 3^{-1/2} = \frac{1}{3^{1/2}} \]

2. Recognize that \( 3^{1/2} \) is the square root of 3: \[ 3^{1/2} = \sqrt{3} \]

3. Substitute this back into the expression: \[ 3^{-1/2} = \frac{1}{\sqrt{3}} \]

Thus, an equivalent expression for \( 3^{-1/2} \) is \( \frac{1}{\sqrt{3}} \).