Question

Use the properties of exponents to generate an equivalent expression for 3√8/2√
.

Answer 1

so its 2^ -1/2?

Answer 2

WHAT IS THE ANSWER PLS HELP

Answer 3

Use the Quotient Property and Negative Exponent Property to generate an equivalent expression for √49 / 7^−3
. What will the rational exponent be for the new expression?(1 point)
and were i need to put the answer a 7 is placed

Answer 4

Consider the equation 43⋅(64−−√3)2=46
. Is this equation true or false? Enter 1 for true or 2 for false.

Answer 5

To simplify the expression \( \frac{3\sqrt{8}}{2\sqrt{}} \), let’s first clarify that you seem to have a missing term under the second square root. Assuming the denominator is a positive real number \( x \), we can denote the expression as \( \frac{3\sqrt{8}}{2\sqrt{x}} \).

We can simplify \( \sqrt{8} \) first:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}.
\]

Now, substituting this back into the expression:
\[
\frac{3\sqrt{8}}{2\sqrt{x}} = \frac{3(2\sqrt{2})}{2\sqrt{x}}.
\]

This can be simplified further:
\[
= \frac{6\sqrt{2}}{2\sqrt{x}}.
\]

Now, divide the numerator and the denominator by 2:
\[
= \frac{3\sqrt{2}}{\sqrt{x}}.
\]

Using the property of exponents that relates square roots to fractional exponents, we can express \( \sqrt{x} \) as \( x^{1/2} \):
\[
= 3 \cdot \frac{\sqrt{2}}{x^{1/2}} = 3 \cdot 2^{1/2} \cdot x^{-1/2}.
\]

Putting it all together, we can express it as:
\[
3 \cdot 2^{1/2} \cdot x^{-1/2} = 3\sqrt{2} x^{-1/2}.
\]

Thus, the equivalent expression for \( \frac{3\sqrt{8}}{2\sqrt{x}} \) is:
\[
3 \sqrt{2} x^{-1/2}.
\]

If you intended for the second square root to be something specific, please provide that information!

Answer 6

The expression you've presented, \( \frac{3\sqrt{8}}{2\sqrt{x}} \), simplifies to \( 3\sqrt{2} x^{-1/2} \), as previously discussed.

Now, if you're looking to express the square root of 2 with a negative exponent, the connection is as follows:

\[
\sqrt{2} = 2^{1/2}.
\]

So if you want to express \( \sqrt{2} \) as an exponent, it would be \( 2^{1/2} \), not \( 2^{-1/2} \).

However, if you were trying to express \( \frac{1}{\sqrt{2}} \) in exponential form, then that would be:

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

To summarize:
- \( \sqrt{2} = 2^{1/2} \)
- \( \frac{1}{\sqrt{2}} = 2^{-1/2} \)

If you have any further clarifications or if there's an extra context you would like to add, please let me know!

Answer 7

I apologize for the confusion earlier. Let's clarify the expression and simplify it clearly.

You provided the expression \( \frac{3\sqrt{8}}{2\sqrt{}} \). Assuming you meant \( \frac{3\sqrt{8}}{2\sqrt{x}} \) (with a variable \( x \) under the second square root), let’s simplify this step-by-step:

### Step 1: Simplify \( \sqrt{8} \)

The square root of 8 can be simplified as follows:
\[
\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}.
\]

### Step 2: Substitute back into the expression

Now substitute \( \sqrt{8} \) back into the expression:
\[
\frac{3\sqrt{8}}{2\sqrt{x}} = \frac{3(2\sqrt{2})}{2\sqrt{x}} = \frac{6\sqrt{2}}{2\sqrt{x}}.
\]

### Step 3: Simplify further

Now, divide 6 by 2:
\[
= \frac{6\sqrt{2}}{2\sqrt{x}} = 3\frac{\sqrt{2}}{\sqrt{x}}.
\]

### Step 4: Use properties of exponents

Next, we can use the property of exponents to express the square roots as fractional exponents:
\[
\sqrt{x} = x^{1/2}.
\]
Thus, we have:
\[
= 3 \cdot \frac{\sqrt{2}}{x^{1/2}}.
\]

### Step 5: Expressing with exponents

Now \( \frac{\sqrt{2}}{x^{1/2}} \) can be rewritten using exponents:
\[
= 3 \cdot 2^{1/2} \cdot x^{-1/2}.
\]

### Final Result

So the final simplified expression is:
\[
\frac{3\sqrt{8}}{2\sqrt{x}} = 3 \cdot 2^{1/2} \cdot x^{-1/2}.
\]

To answer your question more simply: **the simplified expression is** \( 3 \cdot \frac{\sqrt{2}}{\sqrt{x}} \) or equivalently \( 3 \cdot 2^{1/2} \cdot x^{-1/2} \).

If you meant something different or if the denominator was supposed to be another specific value, please clarify and I'd be happy to help!

Answer 8

To simplify the expression \( \frac{\sqrt{49}}{7^{-3}} \) using the Quotient Property and Negative Exponent Property:

### Step 1: Simplify the square root

First, we simplify \( \sqrt{49} \):
\[
\sqrt{49} = 7.
\]

### Step 2: Substitute into the expression

Now, replace \( \sqrt{49} \) in the expression:
\[
\frac{\sqrt{49}}{7^{-3}} = \frac{7}{7^{-3}}.
\]

### Step 3: Use the Quotient Property

The Quotient Property states that \( \frac{a^m}{a^n} = a^{m-n} \). Thus, we can simplify:
\[
\frac{7}{7^{-3}} = 7^{1 - (-3)} = 7^{1 + 3} = 7^{4}.
\]

### Step 4: State the exponent

The rational exponent for the new expression is \( 4 \).

### Final Answer

- The simplified expression is \( 7^{4} \).
- The rational exponent is \( 4 \).

If you need to specify where to place the answer, you can put the number \( 4 \) where indicated by the placeholder "7."

Answer 9

To determine if the equation \( 43 \cdot (\sqrt{64})^3 = 46 \) is true or false, we will first simplify both sides of the equation.

1. **Simplify the left side**:
\[
\sqrt{64} = 8.
\]
Therefore, we have:
\[
(\sqrt{64})^3 = 8^3 = 512.
\]
Now substituting this back into the equation gives us:
\[
43 \cdot 512.
\]

2. **Calculate \( 43 \cdot 512 \)**:
\[
43 \cdot 512 = 21976.
\]

3. **Now compare to the right side**:
The right side of the equation is \( 46 \).

So, we need to check if:
\[
21976 = 46.
\]

This is clearly **not true**.

Hence, the answer is **2 for false**.