Use the Negative Exponent Rule to generate an equivalent expression to 3 −1/2

The Negative Exponent Rule states that \( a^{-n} = \frac{1}{a^n} \).

For the expression \( 3^{-1/2} \), we can apply this rule:

\[
3^{-1/2} = \frac{1}{3^{1/2}}
\]

Since \( 3^{1/2} \) is the square root of 3, we can write this as:

\[
3^{-1/2} = \frac{1}{\sqrt{3}}
\]

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

so the answer is 1/3?

No, the equivalent expression for \( 3^{-1/2} \) is not \( \frac{1}{3} \). The correct answer is:

\[
3^{-1/2} = \frac{1}{\sqrt{3}}
\]

This means that \( 3^{-1/2} \) is equal to the reciprocal of the square root of 3, not \( \frac{1}{3} \). So to clarify:

- \( 3^{-1/2} = \frac{1}{\sqrt{3}} \) (This is the correct equivalent expression)
- \( \frac{1}{3} \) is not correct in this context.

can you show the answer in a diffrent way

Sure! Let’s express \( 3^{-1/2} \) step by step using a different approach.

1. **Understanding the Expression**: The expression \( 3^{-1/2} \) can be broken down as follows:
- The negative exponent indicates that we take the reciprocal.
- The exponent \( \frac{1}{2} \) signifies that we are taking the square root.

2. **Using the Definition of Negative Exponents**:
\[
3^{-1/2} = \frac{1}{3^{1/2}}
\]

3. **Recognizing the Square Root**: The expression \( 3^{1/2} \) is equivalent to \( \sqrt{3} \):
\[
3^{1/2} = \sqrt{3}
\]

4. **Combining the Steps**: Thus, we substitute back:
\[
3^{-1/2} = \frac{1}{\sqrt{3}}
\]

Therefore, the expression \( 3^{-1/2} \) is equivalent to \( \frac{1}{\sqrt{3}} \).

In summary:
\[
3^{-1/2} \equiv \frac{1}{\sqrt{3}}
\]

This shows the connection between the negative exponent and the square root clearly!

how would i put that in like what is this 3^{-1/2} \equiv \frac{1}{\sqrt{3}}

You can express the relationship clearly by using the notation that links the two sides, such as "is equivalent to," "equals," or simply stating the transformation. Here are a few ways to phrase it:

1. **Using "is equal to"**:
\[
3^{-1/2} \text{ is equal to } \frac{1}{\sqrt{3}}
\]

2. **Using "is equivalent to"**:
\[
3^{-1/2} \text{ is equivalent to } \frac{1}{\sqrt{3}}
\]

3. **Using "can be expressed as"**:
\[
3^{-1/2} \text{ can be expressed as } \frac{1}{\sqrt{3}}
\]

4. **Using simple equality**:
\[
3^{-1/2} = \frac{1}{\sqrt{3}}
\]

Any of these phrases can effectively convey that \( 3^{-1/2} \) and \( \frac{1}{\sqrt{3}} \) represent the same value.

If you want a more concise statement for presentation, you could say:
\[
3^{-1/2} \equiv \frac{1}{\sqrt{3}}
\]
This is a clear mathematical way to indicate that both expressions are equivalent.