Sure, let's simplify the given expression step-by-step to get the final result.
Consider the initial expression:
[tex]\[
\frac{-5 w^4 y^{-2}}{-15 w^{-6} y^2}
\][/tex]
### Step 1: Simplify the Coefficients
First, simplify the coefficients [tex]\(-5\)[/tex] and [tex]\(-15\)[/tex]:
[tex]\[
\frac{-5}{-15} = \frac{1}{3}
\][/tex]
### Step 2: Simplify the [tex]\( w \)[/tex] Terms
Next, use the exponent rule for division [tex]\( \frac{a^m}{a^n} = a^{m-n} \)[/tex] to simplify the [tex]\( w \)[/tex] terms:
[tex]\[
\frac{w^4}{w^{-6}} = w^{4 - (-6)} = w^{4 + 6} = w^{10}
\][/tex]
### Step 3: Simplify the [tex]\( y \)[/tex] Terms
Similarly, use the exponent rule for division to simplify the [tex]\( y \)[/tex] terms:
[tex]\[
\frac{y^{-2}}{y^2} = y^{-2 - 2} = y^{-4}
\][/tex]
### Step 4: Combine the Results
Combine all these simplified parts:
[tex]\[
\frac{1}{3} \cdot w^{10} \cdot y^{-4}
\][/tex]
Since [tex]\(y^{-4}\)[/tex] is the same as [tex]\( \frac{1}{y^4} \)[/tex], we can write the expression as:
[tex]\[
\frac{w^{10}}{3 y^4}
\][/tex]
Therefore, the simplified and final expression is:
[tex]\[
\boxed{\frac{w^{10}}{3 y^4}}
\][/tex]
