Simplify ((14c^2f^5)/(9a^2))÷((35cf^4)/(18ab^3))

$\frac{14 c^{2} f^{5}}{9 a^{2}} \div \frac{35 c f^{4}}{18 a b^{3}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{14 c^{2} f^{5}}{9 a^{2}} \cdot \frac{18 a b^{3}}{35 c f^{4}}$

Combine.

$\frac{14 c^{2} f^{5} (18 a b^{3})}{9 a^{2} (35 c f^{4})}$

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

Factor $7$ out of $14 c^{2} f^{5} (18 a b^{3})$ .

$\frac{7 (2 c^{2} f^{5} (18 a b^{3}))}{9 a^{2} (35 c f^{4})}$

Cancel the common factors.

Factor $7$ out of $9 a^{2} (35 c f^{4})$ .

$\frac{7 (2 c^{2} f^{5} (18 a b^{3}))}{7 (9 a^{2} (5 c f^{4}))}$

Cancel the common factor.

$\frac{7 (2 c^{2} f^{5} (18 a b^{3}))}{7 (9 a^{2} (5 c f^{4}))}$

Rewrite the expression.

$\frac{2 c^{2} f^{5} (18 a b^{3})}{9 a^{2} (5 c f^{4})}$

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

Factor $c$ out of $2 c^{2} f^{5} (18 a b^{3})$ .

$\frac{c (2 c f^{5} (18 a b^{3}))}{9 a^{2} (5 c f^{4})}$

Cancel the common factors.

Factor $c$ out of $9 a^{2} (5 c f^{4})$ .

$\frac{c (2 c f^{5} (18 a b^{3}))}{c (9 a^{2} (5 f^{4}))}$

Cancel the common factor.

$\frac{c (2 c f^{5} (18 a b^{3}))}{c (9 a^{2} (5 f^{4}))}$

Rewrite the expression.

$\frac{2 c f^{5} (18 a b^{3})}{9 a^{2} (5 f^{4})}$

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

Factor $f^{4}$ out of $2 c f^{5} (18 a b^{3})$ .

$\frac{f^{4} (2 c f (18 a b^{3}))}{9 a^{2} (5 f^{4})}$

Cancel the common factors.

Factor $f^{4}$ out of $9 a^{2} (5 f^{4})$ .

$\frac{f^{4} (2 c f (18 a b^{3}))}{f^{4} (9 a^{2} \cdot (5))}$

Cancel the common factor.

$\frac{f^{4} (2 c f (18 a b^{3}))}{f^{4} (9 a^{2} \cdot (5))}$

Rewrite the expression.

$\frac{2 c f (18 a b^{3})}{9 a^{2} \cdot (5)}$

Cancel the common factor of $18$ and $9$ .

Factor $9$ out of $2 c f (18 a b^{3})$ .

$\frac{9 (2 c f (2 a b^{3}))}{9 a^{2} \cdot (5)}$

Cancel the common factors.

Factor $9$ out of $9 a^{2} \cdot (5)$ .

$\frac{9 (2 c f (2 a b^{3}))}{9 (a^{2} \cdot (5))}$

Cancel the common factor.

$\frac{9 (2 c f (2 a b^{3}))}{9 (a^{2} \cdot (5))}$

Rewrite the expression.

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

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

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

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

Cancel the common factors.

Factor $a$ out of $a^{2} \cdot (5)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $2$ by adding the exponents.

Move $2$ .

$\frac{2 \cdot 2 c f b^{3}}{a \cdot 5}$

Multiply $2$ by $2$ .

$\frac{2^{2} c f b^{3}}{a \cdot 5}$

Raise $2$ to the power of $2$ .

$\frac{4 c f b^{3}}{a \cdot 5}$

Move $5$ to the left of $a$ .

$\frac{4 c f b^{3}}{5 a}$

Simplify ((14c^2f^5)/(9a^2))÷((35cf^4)/(18ab^3))

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