Simplify (5/(4x))/((7x^3)/2)

$\frac{\frac{5}{4 x}}{\frac{7 x^{3}}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{4 x} \cdot \frac{2}{7 x^{3}}$

Combine.

$\frac{5 \cdot 2}{4 x (7 x^{3})}$

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

Move $x^{3}$ .

$\frac{5 \cdot 2}{4 (x^{3} x) \cdot 7}$

Multiply $x^{3}$ by $x$ .

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

$\frac{5 \cdot 2}{4 (x^{3} x^{1}) \cdot 7}$

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

$\frac{5 \cdot 2}{4 x^{3 + 1} \cdot 7}$

Add $3$ and $1$ .

$\frac{5 \cdot 2}{4 x^{4} \cdot 7}$

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

Factor $2$ out of $5 \cdot 2$ .

$\frac{2 \cdot 5}{4 x^{4} \cdot 7}$

Cancel the common factors.

Factor $2$ out of $4 x^{4} \cdot 7$ .

$\frac{2 \cdot 5}{2 (2 x^{4} \cdot 7)}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 (2 x^{4} \cdot 7)}$

Rewrite the expression.

$\frac{5}{2 x^{4} \cdot 7}$

Multiply $7$ by $2$ .

$\frac{5}{14 x^{4}}$