Simplify (2/(3x^3))÷((4x^3)/3)

$\frac{2}{3 x^{3}} \div \frac{4 x^{3}}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

$\frac{2 \cdot 3}{3 x^{6} \cdot 4}$

Step 4

Cancel the common factor of $2$ and $4$ .

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

$\frac{2 (3)}{3 x^{6} \cdot 4}$

Cancel the common factors.

Factor $2$ out of $3 x^{6} \cdot 4$ .

$\frac{2 (3)}{2 (3 x^{6} \cdot 2)}$

Cancel the common factor.

$\frac{2 \cdot 3}{2 (3 x^{6} \cdot 2)}$

Rewrite the expression.

$\frac{3}{3 x^{6} \cdot 2}$

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{3 x^{6} \cdot 2}$

Rewrite the expression.

$\frac{1}{x^{6} \cdot 2}$

Step 6

Move $2$ to the left of $x^{6}$ .

$\frac{1}{2 x^{6}}$