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

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

Factor $7$ out of $7 x^{4} (12 y^{4})$ .

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

Cancel the common factors.

Factor $7$ out of $24 y^{5} (21 x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Factor $x$ out of $x^{4} (12 y^{4})$ .

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

Cancel the common factors.

Factor $x$ out of $24 y^{5} (3 x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $12$ and $24$ .

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

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

Cancel the common factors.

Factor $12$ out of $24 y^{5} \cdot (3)$ .

$\frac{12 (x^{3} (y^{4}))}{12 (2 y^{5} \cdot 3)}$

Cancel the common factor.

$\frac{12 (x^{3} (y^{4}))}{12 (2 y^{5} \cdot 3)}$

Rewrite the expression.

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

Step 6

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

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

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

Cancel the common factors.

Factor $y^{4}$ out of $2 y^{5} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Multiply $3$ by $2$ .

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

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

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