Simplify (27a^3)÷((18a^4)/(7b^2))

$27 a^{3} \div \frac{18 a^{4}}{7 b^{2}}$

To divide by a fraction, multiply by its reciprocal.

$27 a^{3} \frac{7 b^{2}}{18 a^{4}}$

Cancel the common factor of $9 a^{3}$ .

Factor $9 a^{3}$ out of $27 a^{3}$ .

$9 a^{3} (3) \frac{7 b^{2}}{18 a^{4}}$

Factor $9 a^{3}$ out of $18 a^{4}$ .

$9 a^{3} (3) \frac{7 b^{2}}{9 a^{3} (2 a)}$

Cancel the common factor.

$9 a^{3} \cdot 3 \frac{7 b^{2}}{9 a^{3} (2 a)}$

Rewrite the expression.

$3 \frac{7 b^{2}}{2 a}$

Combine $3$ and $\frac{7 b^{2}}{2 a}$ .

$\frac{3 (7 b^{2})}{2 a}$

Multiply $7$ by $3$ .

$\frac{21 b^{2}}{2 a}$