a. $$ \frac{v^{5}}{v^{2}} \quad $$ c. $$ \frac{20 v^{8}}{5 v} $$ b. $$ \frac{v^{9}}{v^{4}} $$ d. $$ \frac{44 v^{7}}{11 v^{6}} $$

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**a.**  
We simplify $$ \frac{v^{5}}{v^{2}} $$ using the quotient rule for exponents:  
$$
\frac{v^{5}}{v^{2}} = v^{5-2} = v^{3}.
$$

**b.**  
Similarly, for $$ \frac{v^{9}}{v^{4}} $$, we have:  
$$
\frac{v^{9}}{v^{4}} = v^{9-4} = v^{5}.
$$

**c.**  
For $$ \frac{20 v^{8}}{5 v} $$, first simplify the coefficients and then the exponents:  
$$
\frac{20}{5} = 4, \quad \text{and} \quad \frac{v^{8}}{v} = v^{8-1} = v^{7}.
$$  
Thus,  
$$
\frac{20 v^{8}}{5 v} = 4v^{7}.
$$

**d.**  
In $$ \frac{44 v^{7}}{11 v^{6}} $$, we simplify as follows:  
$$
\frac{44}{11} = 4, \quad \text{and} \quad \frac{v^{7}}{v^{6}} = v^{7-6} = v.
$$  
Thus,  
$$
\frac{44 v^{7}}{11 v^{6}} = 4v.
$$
a. $$ v^{3} $$ b. $$ v^{5} $$ c. $$ 4v^{7} $$ d. $$ 4v $$

a. c.
b.
d.

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