Simplify (3x^3)/((6x^4)(4x^5))

$\frac{3 x^{3}}{(6 x^{4}) (4 x^{5})}$

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{3 x^{3}}{6 (x^{5} x^{4}) \cdot 4}$

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

$\frac{3 x^{3}}{6 x^{5 + 4} \cdot 4}$

Add $5$ and $4$ .

$\frac{3 x^{3}}{6 x^{9} \cdot 4}$

Cancel the common factor of $3$ and $6$ .

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

$\frac{3 (x^{3})}{6 x^{9} \cdot 4}$

Cancel the common factors.

Factor $3$ out of $6 x^{9} \cdot 4$ .

$\frac{3 (x^{3})}{3 (2 x^{9} \cdot 4)}$

Cancel the common factor.

$\frac{3 x^{3}}{3 (2 x^{9} \cdot 4)}$

Rewrite the expression.

$\frac{x^{3}}{2 x^{9} \cdot 4}$

Cancel the common factor of $x^{3}$ and $x^{9}$ .

Multiply by $1$ .

$\frac{x^{3} \cdot 1}{2 x^{9} \cdot 4}$

Cancel the common factors.

Factor $x^{3}$ out of $2 x^{9} \cdot 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 x^{6} \cdot 4}$

Multiply $4$ by $2$ .

$\frac{1}{8 x^{6}}$