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?
8k^4 - 2k + 2/k^3
8k^4 + 2/k^3
8k^10 - 2k^6 + 2/k^3
8k^4 - 2 + 2/k^3
To create an equivalent form of the rational expression, we can factor out the greatest common factor from all the terms in the numerator. In this case, the greatest common factor is 14:
56k^7 - 14k^3 + 14 = 14(4k^7 - k^3 + 1)
Now, we can simplify the rational expression:
(14(4k^7 - k^3 + 1))/(7k^3)
= (2(4k^7 - k^3 + 1))/(k^3)
= (8k^7 - 2k^3 + 2)/(k^3)
Therefore, the correct equivalent form is:
8k^7 - 2k^3 + 2/k^3
To create an equivalent form of the given rational expression, let's simplify it step by step.
The original rational expression is:
56k^7 - 14k^3 + 14 / 7k^3
First, we can observe that 14 is a common factor in the numerator and denominator. We can simplify it as follows:
= (14)(4k^7 - k^3 + 1) / (7k^3)
Next, we notice that there is a common factor of k^3 in the numerator. We can factor it out:
= (14)(k^3)(4k^4 - 1 + 1 / k^3) / (7k^3)
Simplifying further:
= (2)(7)(k^3)(4k^4 - 1 + 1 / k^3) / (7k^3)
= 2(4k^4 - 1 + 1 / k^3)
= 8k^4 - 2 + 2 / k^3
Therefore, the correct equivalent form of the rational expression is:
8k^4 - 2 + 2 / k^3
Hence, the option "8k^4 - 2 + 2/k^3" is the correct equivalent form.
To find the correct equivalent form of the rational expression, we need to simplify it.
The given expression is: 56k^7 - 14k^3 + 14 / 7k^3
To simplify it, let's factor out the greatest common factor (GCF) from the first two terms:
GCF of 56k^7 and -14k^3 is 14k^3.
So, we can rewrite the expression as: 14k^3(4k^4 - 1) + 14 / 7k^3
Now, let's simplify the second part of the expression, which is 14 / 7k^3.
14 / 7 = 2, so the expression becomes: 14k^3(4k^4 - 1) + 2 / k^3
Finally, we can distribute the 14k^3 into the (4k^4 - 1) term, which gives us:
(14k^3 * 4k^4) - (14k^3 * 1) + 2 / k^3
Simplifying further:
56k^7 - 14k^3 + 2 / k^3
Therefore, the correct equivalent form of the rational expression is 56k^7 - 14k^3 + 2 / k^3.
None of the provided options match the correct equivalent form.