Sure, let's simplify the given expression step-by-step:
The expression given is:
[tex]\[
\frac{y^{-3}}{4 y^6}
\][/tex]
Step 1: Combine the exponents of [tex]\( y \)[/tex] in the numerator and denominator. Recall that when dividing powers with the same base, you subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{y^{-3}}{4 y^6} = \frac{y^{-3}}{4 \cdot y^6} = \frac{1}{4} \cdot y^{-3 - 6}
\][/tex]
Step 2: Now, simplify the exponent:
[tex]\[
-3 - 6 = -9
\][/tex]
So, we have:
[tex]\[
\frac{1}{4} \cdot y^{-9} = \frac{1}{4 y^9}
\][/tex]
Therefore, the simplified form of the expression is:
[tex]\[
\frac{1}{4 y^9}
\][/tex]
So, the correct answer is:
[tex]\[
\frac{1}{4 y^9}
\][/tex]
