Simplify ((x^3)/5)÷(2/(5x^2))

$\frac{x^{3}}{5} \div \frac{2}{5 x^{2}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{3}}{5} \cdot \frac{5 x^{2}}{2}$

Combine.

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

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{x^{2} x^{3} \cdot 5}{5 \cdot 2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{2 + 3} \cdot 5}{5 \cdot 2}$

Add $2$ and $3$ .

$\frac{x^{5} \cdot 5}{5 \cdot 2}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{x^{5} \cdot 5}{5 \cdot 2}$

Rewrite the expression.

$\frac{x^{5}}{2}$