Simplify ((14m^4)/(3m))÷((7m^2)/(18m^5))

$\frac{14 m^{4}}{3 m} \div \frac{7 m^{2}}{18 m^{5}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{14 m^{4}}{3 m} \cdot \frac{18 m^{5}}{7 m^{2}}$

Step 2

Combine.

$\frac{14 m^{4} (18 m^{5})}{3 m (7 m^{2})}$

Step 3

Multiply $m^{4}$ by $m^{5}$ by adding the exponents.

Move $m^{5}$ .

$\frac{14 (m^{5} m^{4}) \cdot 18}{3 m (7 m^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{14 m^{5 + 4} \cdot 18}{3 m (7 m^{2})}$

Add $5$ and $4$ .

$\frac{14 m^{9} \cdot 18}{3 m (7 m^{2})}$

Step 4

Multiply $m$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$\frac{14 m^{9} \cdot 18}{3 (m^{2} m) \cdot 7}$

Multiply $m^{2}$ by $m$ .

Raise $m$ to the power of $1$ .

$\frac{14 m^{9} \cdot 18}{3 (m^{2} m^{1}) \cdot 7}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{14 m^{9} \cdot 18}{3 m^{2 + 1} \cdot 7}$

Add $2$ and $1$ .

$\frac{14 m^{9} \cdot 18}{3 m^{3} \cdot 7}$

Step 5

Cancel the common factor of $14$ and $7$ .

Factor $7$ out of $14 m^{9} \cdot 18$ .

$\frac{7 (2 m^{9} \cdot 18)}{3 m^{3} \cdot 7}$

Cancel the common factors.

Factor $7$ out of $3 m^{3} \cdot 7$ .

$\frac{7 (2 m^{9} \cdot 18)}{7 \cdot (3 m^{3})}$

Cancel the common factor.

$\frac{7 (2 m^{9} \cdot 18)}{7 \cdot (3 m^{3})}$

Rewrite the expression.

$\frac{2 m^{9} \cdot 18}{3 m^{3}}$

Step 6

Cancel the common factor of $m^{9}$ and $m^{3}$ .

Factor $m^{3}$ out of $2 m^{9} \cdot 18$ .

$\frac{m^{3} (2 m^{6} \cdot 18)}{3 m^{3}}$

Cancel the common factors.

Factor $m^{3}$ out of $3 m^{3}$ .

$\frac{m^{3} (2 m^{6} \cdot 18)}{m^{3} \cdot 3}$

Cancel the common factor.

$\frac{m^{3} (2 m^{6} \cdot 18)}{m^{3} \cdot 3}$

Rewrite the expression.

$\frac{2 m^{6} \cdot 18}{3}$

Step 7

Cancel the common factor of $18$ and $3$ .

Factor $3$ out of $2 m^{6} \cdot 18$ .

$\frac{3 (2 m^{6} \cdot 6)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 m^{6} \cdot 6)}{3 (1)}$

Cancel the common factor.

$\frac{3 (2 m^{6} \cdot 6)}{3 \cdot 1}$

Rewrite the expression.

$\frac{2 m^{6} \cdot 6}{1}$

Divide $2 m^{6} \cdot 6$ by $1$ .

$2 m^{6} \cdot 6$

Step 8

Multiply $6$ by $2$ .

$12 m^{6}$

Simplify ((14m^4)/(3m))÷((7m^2)/(18m^5))

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