Divide ((7x^4)/(24y^5))/((21x)/(12y^4))

$\frac{\frac{7 x^{4}}{24 y^{5}}}{\frac{21 x}{12 y^{4}}}$

Step 1

Cancel the common factor of $21$ and $12$ .

Factor $3$ out of $21 x$ .

$\frac{\frac{7 x^{4}}{24 y^{5}}}{\frac{3 (7 x)}{12 y^{4}}}$

Cancel the common factors.

Factor $3$ out of $12 y^{4}$ .

$\frac{\frac{7 x^{4}}{24 y^{5}}}{\frac{3 (7 x)}{3 (4 y^{4})}}$

Cancel the common factor.

$\frac{\frac{7 x^{4}}{24 y^{5}}}{\frac{3 (7 x)}{3 (4 y^{4})}}$

Rewrite the expression.

$\frac{\frac{7 x^{4}}{24 y^{5}}}{\frac{7 x}{4 y^{4}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 x^{4}}{24 y^{5}} \cdot \frac{4 y^{4}}{7 x}$

Step 3

Combine.

$\frac{7 x^{4} (4 y^{4})}{24 y^{5} (7 x)}$

Step 4

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{4} (4 y^{4})}{24 y^{5} (7 x)}$

Rewrite the expression.

$\frac{x^{4} (4 y^{4})}{24 y^{5} (x)}$

Step 5

Cancel the common factor of $x^{4}$ and $x$ .

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

$\frac{x (x^{3} (4 y^{4}))}{24 y^{5} (x)}$

Cancel the common factors.

Factor $x$ out of $24 y^{5} (x)$ .

$\frac{x (x^{3} (4 y^{4}))}{x (24 y^{5})}$

Cancel the common factor.

$\frac{x (x^{3} (4 y^{4}))}{x (24 y^{5})}$

Rewrite the expression.

$\frac{x^{3} (4 y^{4})}{24 y^{5}}$

Step 6

Cancel the common factor of $4$ and $24$ .

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

$\frac{4 (x^{3} (y^{4}))}{24 y^{5}}$

Cancel the common factors.

Factor $4$ out of $24 y^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Cancel the common factor of $y^{4}$ and $y^{5}$ .

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

$\frac{y^{4} x^{3}}{6 y^{5}}$

Cancel the common factors.

Factor $y^{4}$ out of $6 y^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide ((7x^4)/(24y^5))/((21x)/(12y^4))

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