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5 answers
The Negative Exponent Rule states that \( a^{-n} = \frac{1}{a^n} \).
For the expression \( 3^{-1/2} \), we can apply the rule as follows:
\[ 3^{-1/2} = \frac{1}{3^{1/2}} \]
Now, \( 3^{1/2} \) is equivalent to the square root of 3:
\[ 3^{-1/2} = \frac{1}{\sqrt{3}} \]
So, an equivalent expression to \( 3^{-1/2} \) is:
\[ \frac{1}{\sqrt{3}} \]
The actual answer for the expression \( 3^{-1/2} \), using the Negative Exponent Rule, is:
\[ \frac{1}{\sqrt{3}} \]
If you want a numerical approximation, it is approximately:
\[ \frac{1}{\sqrt{3}} \approx 0.577 \]
So, in summary:
\[ 3^{-1/2} = \frac{1}{\sqrt{3}} \approx 0.577 \]
The expression \(\frac{1}{\sqrt{3}}\) can be approximated numerically.
To calculate it explicitly:
\[ \frac{1}{\sqrt{3}} \approx 0.57735 \]
If you want to express it in a form without a square root in the denominator (to rationalize the denominator), you can multiply the numerator and denominator by \(\sqrt{3}\):
\[ \frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3} \]
So, \(\frac{1}{\sqrt{3}}\) can also be expressed as \(\frac{\sqrt{3}}{3}\) or approximately \(0.57735\).
