Simplify (5/(3x))÷(2/(5x^3))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $5 (5 x^{3})$ .

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

Cancel the common factors.

Factor $x$ out of $3 x \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the expression.

Multiply $5$ by $5$ .

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

Multiply $3$ by $2$ .

$\frac{5^{2} x^{2}}{6}$

Raise $5$ to the power of $2$ .

$\frac{25 x^{2}}{6}$