Question

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

8k4− 2k +2k3
8k4− 2k +2k3

8k4 − 2 + 2k3
8k4 − 2 + 2k3

8k4+2k3
8 k to the 4th power plus the fraction with numerator 2 and denominator k cubed

8k10 − 2k6 +2k3

Answer 1

To create an equivalent form of the rational expression \( \frac{56k^7 - 14k^3 + 14}{7k^3} \), we can simplify it by dividing each term in the numerator by \( 7k^3 \):

1. **Divide the first term**:
\[
\frac{56k^7}{7k^3} = 8k^{7-3} = 8k^4
\]

2. **Divide the second term**:
\[
\frac{-14k^3}{7k^3} = -2
\]

3. **Divide the third term**:
\[
\frac{14}{7k^3} = \frac{2}{k^3}
\]

Putting these results together, we get:
\[
\frac{56k^7 - 14k^3 + 14}{7k^3} = 8k^4 - 2 + \frac{2}{k^3}
\]

Now, let's look at the options given:

1. \( 8k^4− 2k + 2k^3 \)
2. \( 8k^4 − 2 + 2k^3 \)
3. \( 8k^4+2k^3 \)
4. \( 8k^{10} − 2k^6 +2k^3 \)

The correct equivalent form that matches our simplification is:

**\( 8k^4 - 2 + \frac{2}{k^3} \)**

However, none of the options presented have exactly \( \frac{2}{k^3} \). But the one closest in terms of non-fractional representation would be:

**\( 8k^4 − 2 + 2k^3 \)**

**Final Answer**: \( 8k^4 − 2 + 2k^3 \) (though this doesn't simplify to the exact \( 2/k^3 \), it seems to be the intended choice).