Simplify ((6x)/5)÷(9/(5x^2))

$\frac{6 x}{5} \div \frac{9}{5 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 x}{5} \cdot \frac{5 x^{2}}{9}$

Step 2

Combine.

$\frac{6 x (5 x^{2})}{5 \cdot 9}$

Step 3

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

Move $x^{2}$ .

$\frac{6 (x^{2} x) \cdot 5}{5 \cdot 9}$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{6 (x^{2} x^{1}) \cdot 5}{5 \cdot 9}$

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

$\frac{6 x^{2 + 1} \cdot 5}{5 \cdot 9}$

Add $2$ and $1$ .

$\frac{6 x^{3} \cdot 5}{5 \cdot 9}$

Step 4

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6 x^{3} \cdot 5$ .

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

Cancel the common factors.

Factor $3$ out of $5 \cdot 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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