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

Answer 1

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 \( \frac{1}{\sqrt{3}} \).

Answer 2

so the answer is 1/3?

Answer 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.

Answer 4

can you show the answer in a diffrent way

Answer 5

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!

Answer 6

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

Answer 7

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.