Algebra Examples

$\frac{8 x^{3}}{9} \div \frac{3}{2 x^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 x^{3}}{9} \cdot \frac{2 x^{2}}{3}$

Step 2

Combine.

$\frac{8 x^{3} (2 x^{2})}{9 \cdot 3}$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$\frac{8 (x^{2} x^{3}) \cdot 2}{9 \cdot 3}$

Step 3.2

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

$\frac{8 x^{2 + 3} \cdot 2}{9 \cdot 3}$

Step 3.3

Add $2$ and $3$ .

$\frac{8 x^{5} \cdot 2}{9 \cdot 3}$

Step 4

Multiply $2$ by $8$ .

$\frac{16 x^{5}}{9 \cdot 3}$

Step 5

Multiply $9$ by $3$ .

$\frac{16 x^{5}}{27}$