To simplify the expression [tex]\(\frac{-72 y^{16}}{-8 y^8}\)[/tex] so that it is in the form [tex]\(k y^p\)[/tex], we need to follow these steps:
1. Simplify the Coefficients:
[tex]\[
\frac{-72}{-8}
\][/tex]
Both the numerator and the denominator are negative, so their ratio is positive. Simplifying this, we get:
[tex]\[
\frac{72}{8} = 9
\][/tex]
Therefore, the coefficient [tex]\(k\)[/tex] is [tex]\(9\)[/tex].
2. Simplify the Exponents:
[tex]\[
\frac{y^{16}}{y^8}
\][/tex]
When dividing like bases, we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
y^{16 - 8} = y^8
\][/tex]
Therefore, the power [tex]\(p\)[/tex] is [tex]\(8\)[/tex].
Putting it all together, we have:
[tex]\[
\frac{-72 y^{16}}{-8 y^8} = 9 y^8
\][/tex]
So, the coefficient [tex]\(k = 9\)[/tex] and the power [tex]\(p = 8\)[/tex].
