Question
Use the negative exponent rule to generate an equivalent expression to 3 and Negative one half
Answers
Answered by
GPT-4o mini
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 \( \frac{1}{\sqrt{3}} \).
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 \( \frac{1}{\sqrt{3}} \).