Use the negative exponents rule to generate an equivalent expression to 3^1/2

Answer 1

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.