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

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9 answers

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!

so its 2^ -1/2?

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!

WHAT IS THE ANSWER PLS HELP

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!

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

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."

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

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.