Statement
When dividing by a fraction, you multiply by the reciprocal.
$$ a \div \frac{b}{c} = a * \frac{c}{b} $$
Proof
Write the fraction using negative exponents.
$$ a \div \frac{b}{c} = a \div (b * c^{-1}) $$
Now write the division using negative exponents as well.
$$ a \div \frac{b}{c} = a * (b * c^{-1})^{-1} $$
Append the powers to the factors.
$$ a \div \frac{b}{c} = a * b^{-1} * (c^{-1})^{-1} $$
$$ a \div \frac{b}{c} = a * b^{-1} * c^1 $$
Finally, write $ b^{-1} * c $ as a fraction again.
$$ a \div \frac{b}{c} = a * \frac{c}{b} $$