Question

Myrna was asked to create an equivalent form of the rational expression 56k7−14k3+147k3
. Which of the following is a correct equivalent form?(1 point)
Responses

8k4−2+2k3
8 superscript k 4 baseline minus 2 plus Start Fraction 2 over k cubed End Fraction

8k4+2k3
8 superscript k 4 baseline plus Start Fraction 2 over k cubed End Fraction

8k4−2k+2k3
8 superscript k 4 baseline minus 2 k plus Start Fraction 2 over k cubed End Fraction

8k10−2k6+2k3

Answer 1

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

Let's start by combining the \( -14k^3 \) and \( +147k^3 \):
\[
-14k^3 + 147k^3 = 133k^3
\]

Now, our expression is:
\[
56k^7 + 133k^3
\]

Next, we can factor out the greatest common factor (GCF) from the expression. The GCF of \( 56k^7 \) and \( 133k^3 \) is \( 7k^3 \):
\[
7k^3(8k^4 + 19)
\]

From here, we can express the equivalent form neatly:
\[
8k^4 + 19
\]

None of the provided responses match this exact equivalent form directly, but if we consider only \( 8k^4 + 2k^3 \), that could represent a different formulation of simplified parts.

Let’s review the provided options:
1. \( 8k^4 - 2 + \frac{2}{k^3} \)
2. \( 8k^4 + \frac{2}{k^3} \)
3. \( 8k^4 - 2k + 2k^3 \)
4. \( 8k^{10} - 2k^6 + 2k^3 \)

Given that:

- The first, third, and fourth options do not adequately reflect a simplification of the expression we derived.
- The second option does not include anything that derives directly from our simplified expression.

Therefore, the equivalent simplified expression is \( 7k^3(8k^4 + 19) \), but unfortunately, none of the given options match this format.

If I have to answer based strictly on responses given, all provided responses do not represent a simplification of \( 56k^7 - 14k^3 + 147k^3\). Thus, the closest you might want to consider is the option without a negative or complex fractions, but nothing strictly is an equivalent transformation.

So, while the best answer cannot be chosen from the options provided, the general path to the simplification is outlined above.