To find the value of the expression [tex]\(\frac{y^3 \cdot k}{y^0}\)[/tex] with the given values [tex]\(h = 8\)[/tex], [tex]\(j = -1\)[/tex], and [tex]\(k = -12\)[/tex], we'll follow these steps:
1. Substitute [tex]\(y\)[/tex] with [tex]\(h\)[/tex]: Since we are not explicitly given a [tex]\(y\)[/tex], we will assume that [tex]\(y = h = 8\)[/tex].
2. Calculate [tex]\(y^3\)[/tex]:
[tex]\[
y^3 = 8^3 = 8 \times 8 \times 8 = 512
\][/tex]
3. Multiply [tex]\(y^3\)[/tex] with [tex]\(k\)[/tex]:
[tex]\[
512 \times (-12) = -6144
\][/tex]
4. Calculate the denominator [tex]\(y^0\)[/tex]:
[tex]\[
y^0 = 8^0 = 1 \quad \text{(Any non-zero number raised to the power of 0 is 1)}
\][/tex]
5. Divide the result from step 3 by the result from step 4:
[tex]\[
\frac{512 \times (-12)}{1} = \frac{-6144}{1} = -6144
\][/tex]
Therefore, the value of the expression [tex]\(\frac{y^3 \cdot k}{y^0}\)[/tex] is [tex]\(-6144\)[/tex]. Hence, none of the provided multiple-choice answers (A, B, C, D) are correct in this context, but since we are tasked to select based on the computed value:
Selecting the correct value, which is [tex]\(-6144\)[/tex], we recognize that there may be a mismatch in provided options versus the calculated outcome. The correct value according to this calculation is [tex]\(-6144\)[/tex].
