Simplify x/((2yx^4)^3)

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

Simplify the denominator.

Apply the product rule to $2 y x^{4}$ .

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

Apply the product rule to $2 y$ .

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

Raise $2$ to the power of $3$ .

$\frac{x}{8 y^{3} {(x^{4})}^{3}}$

Multiply the exponents in ${(x^{4})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x}{8 y^{3} x^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{x}{8 y^{3} x^{12}}$

Cancel the common factor of $x$ and $x^{12}$ .

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

$\frac{x^{1}}{8 y^{3} x^{12}}$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1}{8 y^{3} x^{12}}$

Cancel the common factors.

Factor $x$ out of $8 y^{3} x^{12}$ .

$\frac{x \cdot 1}{x (8 y^{3} x^{11})}$

Cancel the common factor.

$\frac{x \cdot 1}{x (8 y^{3} x^{11})}$

Rewrite the expression.

$\frac{1}{8 y^{3} x^{11}}$