To simplify the expression [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex], let's follow these steps:
### Step 1: Understand the given expression
The expression we want to simplify is [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex].
### Step 2: Apply the properties of exponents
We know that:
[tex]\[ y^{-a} = \frac{1}{y^a} \][/tex]
Using this, we can rewrite [tex]\( y^{-2} \)[/tex] in the numerator:
[tex]\[ \frac{y^{-2}}{3 y^4} = \frac{1}{y^2} \cdot \frac{1}{3 y^4} \][/tex]
### Step 3: Combine the exponents
Since both terms involve [tex]\( y \)[/tex] with exponents, we can use the property of exponents which states:
[tex]\[ \frac{y^m}{y^n} = y^{m-n} \][/tex]
So:
[tex]\[ \frac{1}{y^2 \cdot 3 y^4} = \frac{1}{3 y^{2+4}} = \frac{1}{3 y^6} \][/tex]
### Step 4: Simplified expression
After combining the exponents and simplifying, we get:
[tex]\[ \frac{1}{3 y^6} \][/tex]
Hence, the simplified form of [tex]\(\frac{y^{-2}}{3 y^4}\)[/tex] is [tex]\(\frac{1}{3 y^6}\)[/tex].
So, the correct choice from the given options is:
[tex]\[
\frac{1}{3 y^6}
\][/tex]
