Divide ((7x)/(4y^3))/((21x^3)/(8y))

$\frac{\frac{7 x}{4 y^{3}}}{\frac{21 x^{3}}{8 y}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 x}{4 y^{3}} \cdot \frac{8 y}{21 x^{3}}$

Step 2

Combine.

$\frac{7 x (8 y)}{4 y^{3} (21 x^{3})}$

Step 3

Cancel the common factor of $7$ and $21$ .

Factor $7$ out of $7 x (8 y)$ .

$\frac{7 (x (8 y))}{4 y^{3} (21 x^{3})}$

Cancel the common factors.

Factor $7$ out of $4 y^{3} (21 x^{3})$ .

$\frac{7 (x (8 y))}{7 (4 y^{3} (3 x^{3}))}$

Cancel the common factor.

$\frac{7 (x (8 y))}{7 (4 y^{3} (3 x^{3}))}$

Rewrite the expression.

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

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

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

Step 4

Cancel the common factors.

Factor $x$ out of $4 y^{3} (3 x^{3})$ .

$\frac{x (8 y)}{x (4 y^{3} (3 x^{2}))}$

Cancel the common factor.

$\frac{x (8 y)}{x (4 y^{3} (3 x^{2}))}$

Rewrite the expression.

$\frac{8 y}{4 y^{3} (3 x^{2})}$

$\frac{8 y}{4 y^{3} (3 x^{2})}$

Step 5

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $8 y$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 6

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

Factor $y$ out of $2 y$ .

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

Cancel the common factors.

Factor $y$ out of $y^{3} (3 x^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 7

Move $3$ to the left of $y^{2}$ .

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

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