Simplify (x/9)÷(8/(7x^2))

$\frac{x}{9} \div \frac{8}{7 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x}{9} \cdot \frac{7 x^{2}}{8}$

Step 2

Combine.

$\frac{x (7 x^{2})}{9 \cdot 8}$

Step 3

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

Move $x^{2}$ .

$\frac{x^{2} x \cdot 7}{9 \cdot 8}$

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

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

$\frac{x^{2} x^{1} \cdot 7}{9 \cdot 8}$

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

$\frac{x^{2 + 1} \cdot 7}{9 \cdot 8}$

Add $2$ and $1$ .

$\frac{x^{3} \cdot 7}{9 \cdot 8}$

Step 4

Multiply $9$ by $8$ .

$\frac{x^{3} \cdot 7}{72}$

Step 5

Move $7$ to the left of $x^{3}$ .

$\frac{7 x^{3}}{72}$