Divide ((24a^3)/(35b^2))÷((16a)/(14b^3))

$\frac{24 a^{3}}{35 b^{2}} \div \frac{16 a}{14 b^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{24 a^{3}}{35 b^{2}} \cdot \frac{14 b^{3}}{16 a}$

Step 2

Combine.

$\frac{24 a^{3} (14 b^{3})}{35 b^{2} (16 a)}$

Step 3

Cancel the common factor of $24$ and $16$ .

Factor $8$ out of $24 a^{3} (14 b^{3})$ .

$\frac{8 (3 a^{3} (14 b^{3}))}{35 b^{2} (16 a)}$

Cancel the common factors.

Factor $8$ out of $35 b^{2} (16 a)$ .

$\frac{8 (3 a^{3} (14 b^{3}))}{8 (35 b^{2} (2 a))}$

Cancel the common factor.

$\frac{8 (3 a^{3} (14 b^{3}))}{8 (35 b^{2} (2 a))}$

Rewrite the expression.

$\frac{3 a^{3} (14 b^{3})}{35 b^{2} (2 a)}$

Step 4

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

Factor $a$ out of $3 a^{3} (14 b^{3})$ .

$\frac{a (3 a^{2} (14 b^{3}))}{35 b^{2} (2 a)}$

Cancel the common factors.

Factor $a$ out of $35 b^{2} (2 a)$ .

$\frac{a (3 a^{2} (14 b^{3}))}{a (35 b^{2} \cdot (2))}$

Cancel the common factor.

$\frac{a (3 a^{2} (14 b^{3}))}{a (35 b^{2} \cdot (2))}$

Rewrite the expression.

$\frac{3 a^{2} (14 b^{3})}{35 b^{2} \cdot (2)}$

Step 5

Cancel the common factor of $14$ and $35$ .

Factor $7$ out of $3 a^{2} (14 b^{3})$ .

$\frac{7 (3 a^{2} (2 b^{3}))}{35 b^{2} \cdot (2)}$

Cancel the common factors.

Factor $7$ out of $35 b^{2} \cdot (2)$ .

$\frac{7 (3 a^{2} (2 b^{3}))}{7 (5 b^{2} \cdot 2)}$

Cancel the common factor.

$\frac{7 (3 a^{2} (2 b^{3}))}{7 (5 b^{2} \cdot 2)}$

Rewrite the expression.

$\frac{3 a^{2} (2 b^{3})}{5 b^{2} \cdot 2}$

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 a^{2} (2 b^{3})}{5 b^{2} \cdot 2}$

Rewrite the expression.

$\frac{3 a^{2} (b^{3})}{5 b^{2}}$

Step 7

Cancel the common factor of $b^{3}$ and $b^{2}$ .

Factor $b^{2}$ out of $3 a^{2} (b^{3})$ .

$\frac{b^{2} (3 a^{2} (b))}{5 b^{2}}$

Cancel the common factors.

Factor $b^{2}$ out of $5 b^{2}$ .

$\frac{b^{2} (3 a^{2} (b))}{b^{2} \cdot 5}$

Cancel the common factor.

$\frac{b^{2} (3 a^{2} (b))}{b^{2} \cdot 5}$

Rewrite the expression.

$\frac{3 a^{2} (b)}{5}$

$\frac{3 a^{2} b}{5}$

Divide ((24a^3)/(35b^2))÷((16a)/(14b^3))

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