Ask a New Question
Menu

Myrna was asked to create an equivalent from of the rational expression 56k7−14k3+147k3 . Which of the following is a correct equivalent form?(1 point) Responses 8k4−2+2k3 8 k to the 4th power minus 2 plus the fraction with numerator 2 and denominator k cubed 8k4+2k3 8 k to the 4th power plus the fraction with numerator 2 and denominator k cubed 8k10−2k6+2k3 8 k to the 10th power minus 2 k to the 6th power plus the fraction with numerator 2 and denominator k cubed 8k4−2k+2k3

5 answers

To simplify the rational expression \(56k^7 - 14k^3 + 147k^3\), we first combine like terms.

Combining the terms \( -14k^3\) and \(147k^3\):

\[ -14k^3 + 147k^3 = 133k^3 \]

So, the expression simplifies to:

\[ 56k^7 + 133k^3 \]

Next, we can factor out any common terms. In this case, both terms share a common factor of \(k^3\):

\[ 56k^7 + 133k^3 = k^3(56k^4 + 133) \]

Now let's check the provided options to see which one matches:

  1. \(8k^4 - 2 + 2k^3\) - This does not match our expression.
  2. \(8k^4 + 2k^3\) - This does not match our expression.
  3. \(8k^{10} - 2k^6 + 2k^3\) - This does not match our expression.
  4. \(8k^4 - 2k + 2k^3\) - This does not match our expression.

None of the given options are equivalent to \(k^3(56k^4 + 133)\) or its simplified form.

Since none of the responses match the simplified rational expression of \(56k^7 + 133k^3\) (or the factored form of \(k^3(56k^4 + 133)\)), it seems there might be a misunderstanding or an error in the options provided.

sorry Myrna was asked to create an equivalent from of the rational expression 56k^7-14k^3+14 over 7k^3 . Which of the following is a correct equivalent form?(1 point)

To simplify the expression \( \frac{56k^7 - 14k^3 + 14}{7k^3} \), we follow these steps:

  1. Factor the Numerator: We can factor out the greatest common factor from the numerator:

    \[ 56k^7 - 14k^3 + 14 \]

    Let's look for a common factor in all terms. The greatest common factor (GCF) here is 14.

    \[ 56k^7 = 14 \cdot 4k^7 \] \[ -14k^3 = 14 \cdot (-1)k^3 \] \[ +14 = 14 \cdot 1 \]

    So we can factor 14 out from the numerator:

    \[ 14(4k^7 - k^3 + 1) \]

  2. Rewrite the Expression: Substitute the factored form back into the expression:

    \[ \frac{14(4k^7 - k^3 + 1)}{7k^3} \]

  3. Simplify: The factor of 14 in the numerator and 7 in the denominator simplifies as:

    \[ \frac{14}{7} = 2 \]

    Thus, the expression simplifies to:

    \[ 2 \cdot \frac{4k^7 - k^3 + 1}{k^3} \]

    This can be split into separate fractions:

    \[ 2 \left( \frac{4k^7}{k^3} - \frac{k^3}{k^3} + \frac{1}{k^3} \right) \]

    Simplifying the individual terms gives:

    \[ 2(4k^{7-3} - 1 + \frac{1}{k^3}) = 2(4k^4 - 1 + \frac{1}{k^3}) \]

  4. Final Expression: Therefore, the simplified equivalent form of the expression \( \frac{56k^7 - 14k^3 + 14}{7k^3} \) is:

    \[ 8k^4 - 2 + \frac{2}{k^3} \]

Now, comparing the above simplified form with the provided options, if they follow a similar structure, we can verify which one is equivalent.

Do any of the answer choices appear similar? If you can provide the specific answer choices, I can help identify the correct equivalent form.

Yes thats it!

Great! Based on our simplification, the equivalent form of the rational expression \( \frac{56k^7 - 14k^3 + 14}{7k^3} \) is:

\[ 8k^4 - 2 + \frac{2}{k^3} \]

If this matches one of your answer choices, that would be the correct answer. If you have any further questions or need more assistance, feel free to ask!