Simplify ((3x)/(10a^3))÷(1/(5a^2))

$\frac{3 x}{10 a^{3}} \div \frac{1}{5 a^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x}{10 a^{3}} (5 a^{2})$

Rewrite using the commutative property of multiplication.

$5 \frac{3 x}{10 a^{3}} a^{2}$

Cancel the common factor of $5$ .

Factor $5$ out of $10 a^{3}$ .

$5 \frac{3 x}{5 (2 a^{3})} a^{2}$

Cancel the common factor.

$5 \frac{3 x}{5 (2 a^{3})} a^{2}$

Rewrite the expression.

$\frac{3 x}{2 a^{3}} a^{2}$

Cancel the common factor of $a^{2}$ .

Factor $a^{2}$ out of $2 a^{3}$ .

$\frac{3 x}{a^{2} (2 a)} a^{2}$

Cancel the common factor.

$\frac{3 x}{a^{2} (2 a)} a^{2}$

Rewrite the expression.

$\frac{3 x}{2 a}$