Simplify (4/(3x^7))÷((x-2)/(9x^5))

$\frac{4}{3 x^{7}} \div \frac{x - 2}{9 x^{5}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{4}{3 x^{7}} \cdot \frac{9 x^{5}}{x - 2}$

Cancel the common factor of $3 x^{5}$ .

Factor $3 x^{5}$ out of $3 x^{7}$ .

$\frac{4}{3 x^{5} (x^{2})} \cdot \frac{9 x^{5}}{x - 2}$

Factor $3 x^{5}$ out of $9 x^{5}$ .

$\frac{4}{3 x^{5} (x^{2})} \cdot \frac{3 x^{5} (3)}{x - 2}$

Cancel the common factor.

$\frac{4}{3 x^{5} x^{2}} \cdot \frac{3 x^{5} \cdot 3}{x - 2}$

Rewrite the expression.

$\frac{4}{x^{2}} \cdot \frac{3}{x - 2}$

Multiply $\frac{4}{x^{2}}$ by $\frac{3}{x - 2}$ .

$\frac{4 \cdot 3}{x^{2} (x - 2)}$

Multiply $4$ by $3$ .

$\frac{12}{x^{2} (x - 2)}$