Prove that the Legendre symbol
$$ (\frac{ab^2}{p}) = (\frac{a}{p}) $$
given that $\gcd (a, p) = \gcd (b, p) = 1$.
We use Proposition (7.9), noting that $p \not \mid a$, and $p \not \mid b$.
$$ \begin{align} (\frac{ab^2}{p}) & = (\frac{a}{p}) \times (\frac{b^2}{p}) \\ \\ & = (\frac{a}{p}) \times 1 \\ \\ & = (\frac{a}{p}) \end{align}$$