Certainly! Let's simplify the given expression step-by-step:
[tex]\[
\frac{-12 v^5}{3 v^5}
\][/tex]
### Step 1: Simplify the Coefficients
First, we look at the numerical coefficients in the numerator and the denominator:
[tex]\[
\frac{-12}{3}
\][/tex]
Dividing [tex]\(-12\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
\frac{-12}{3} = -4
\][/tex]
### Step 2: Simplify the Variables
Next, we simplify the variable part of the expression. The variables in the numerator and the denominator are both [tex]\(v^5\)[/tex]:
[tex]\[
\frac{v^5}{v^5}
\][/tex]
Since [tex]\(v^5\)[/tex] divided by [tex]\(v^5\)[/tex] is [tex]\(1\)[/tex] (as long as [tex]\(v \neq 0\)[/tex]):
[tex]\[
\frac{v^5}{v^5} = 1
\][/tex]
### Step 3: Combine the Simplified Parts
Finally, we combine the simplified numerical coefficient and the simplified variable:
[tex]\[
-4 \cdot 1 = -4
\][/tex]
Thus, the simplified result of the given expression is:
[tex]\[
\frac{-12 v^5}{3 v^5} = -4
\][/tex]
So the answer is [tex]\(\boxed{-4}\)[/tex].
