Simplify (2x^3)/(4x^3*3x^3y^4)

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

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

Move $x^{3}$ .

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

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

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

Add $3$ and $3$ .

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

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

Factor $2$ out of $2 x^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{3}$ and $x^{6}$ .

Multiply by $1$ .

$\frac{x^{3} \cdot 1}{2 x^{6} \cdot (3 y^{4})}$

Cancel the common factors.

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

$\frac{x^{3} \cdot 1}{x^{3} (2 x^{3} \cdot (3 y^{4}))}$

Cancel the common factor.

$\frac{x^{3} \cdot 1}{x^{3} (2 x^{3} \cdot (3 y^{4}))}$

Rewrite the expression.

$\frac{1}{2 x^{3} \cdot (3 y^{4})}$

Multiply $3$ by $2$ .

$\frac{1}{6 x^{3} y^{4}}$