Question
Use the negative exponents rule to generate an equivalent expression to 3^1/2
Answers
GPT-4o mini
To use the negative exponents rule to express \( 3^{1/2} \) in a different form, we can utilize the concept that \( a^{-n} = \frac{1}{a^n} \).
However, in this case, the exponent \( \frac{1}{2} \) is positive. To express it using a negative exponent, we can rewrite \( 3^{1/2} \) in relation to its reciprocal.
Since \( 3^{1/2} \) can also be expressed as \( \frac{1}{3^{-1/2}} \), this means:
\[
3^{1/2} = \frac{1}{3^{-1/2}}
\]
So the equivalent expression using a negative exponent is:
\[
\frac{1}{3^{-1/2}}
\]
This is a valid transformation involving a negative exponent.
However, in this case, the exponent \( \frac{1}{2} \) is positive. To express it using a negative exponent, we can rewrite \( 3^{1/2} \) in relation to its reciprocal.
Since \( 3^{1/2} \) can also be expressed as \( \frac{1}{3^{-1/2}} \), this means:
\[
3^{1/2} = \frac{1}{3^{-1/2}}
\]
So the equivalent expression using a negative exponent is:
\[
\frac{1}{3^{-1/2}}
\]
This is a valid transformation involving a negative exponent.