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Determine the following limit$.$

$\underset{w}{lim}\frac{8w^{2}5w7}{\sqrt[\phantom{2}]{16w^{4}5w^3}}$

Select the correct choice, and, if necessary, fill in the answer box to complete your choice

A$.\underset{w}{lim}\frac{8w^{2}5w7}{\sqrt[\phantom{2}]{16w^{4}5w^3}}=($Simplify your answer.$)$

$$

B$.$ The limit does not exist and is neither $$ nor $-$ :