Sure, let's go through the steps to divide the polynomial [tex]\(8y^{\top}\)[/tex] by [tex]\(4y^5\)[/tex].
1. Write down the division: We are given the polynomial [tex]\(8y^{\top}\)[/tex] divided by [tex]\(4y^5\)[/tex].
[tex]\[
\frac{8y^{\top}}{4y^5}
\][/tex]
2. Divide the coefficients: The coefficients are 8 and 4. Dividing these gives:
[tex]\[
\frac{8}{4} = 2
\][/tex]
3. Divide the variables with exponents: Let’s handle the [tex]\(y\)[/tex] terms now. When you divide variables with the same base, you subtract the exponents:
[tex]\[
y^{\top} \div y^5 = y^{\top - 5}
\][/tex]
Since TOP in math usually means highest degree and we are not given the exact value, we'll use a variable [tex]\(n\)[/tex] to represent the exponent higher degree.
Therefore,
[tex]\[
y^{\top - 5} \rightarrow y^{n - 5}
\][/tex]
4. Combine the results: Combining the coefficients and the simplified variable terms, we get:
[tex]\[
2y^{n - 5}
\][/tex]
Placing our final answer in the proper location on the grid:
[tex]\[
2y^{n - 5}
\][/tex]
