Simplify ((10mk^2)/(3c^2d))÷((5m^5)/(6c^2d^2))

$\frac{10 m k^{2}}{3 c^{2} d} \div \frac{5 m^{5}}{6 c^{2} d^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 m k^{2}}{3 c^{2} d} \cdot \frac{6 c^{2} d^{2}}{5 m^{5}}$

Step 2

Combine.

$\frac{10 m k^{2} (6 c^{2} d^{2})}{3 c^{2} d (5 m^{5})}$

Step 3

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 m k^{2} (6 c^{2} d^{2})$ .

$\frac{5 (2 m k^{2} (6 c^{2} d^{2}))}{3 c^{2} d (5 m^{5})}$

Cancel the common factors.

Factor $5$ out of $3 c^{2} d (5 m^{5})$ .

$\frac{5 (2 m k^{2} (6 c^{2} d^{2}))}{5 (3 c^{2} d (m^{5}))}$

Cancel the common factor.

$\frac{5 (2 m k^{2} (6 c^{2} d^{2}))}{5 (3 c^{2} d (m^{5}))}$

Rewrite the expression.

$\frac{2 m k^{2} (6 c^{2} d^{2})}{3 c^{2} d (m^{5})}$

Step 4

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

Factor $m$ out of $2 m k^{2} (6 c^{2} d^{2})$ .

$\frac{m (2 k^{2} (6 c^{2} d^{2}))}{3 c^{2} d (m^{5})}$

Cancel the common factors.

Factor $m$ out of $3 c^{2} d (m^{5})$ .

$\frac{m (2 k^{2} (6 c^{2} d^{2}))}{m (3 c^{2} d (m^{4}))}$

Cancel the common factor.

$\frac{m (2 k^{2} (6 c^{2} d^{2}))}{m (3 c^{2} d (m^{4}))}$

Rewrite the expression.

$\frac{2 k^{2} (6 c^{2} d^{2})}{3 c^{2} d (m^{4})}$

Step 5

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $2 k^{2} (6 c^{2} d^{2})$ .

$\frac{3 (2 k^{2} (2 c^{2} d^{2}))}{3 c^{2} d (m^{4})}$

Cancel the common factors.

Factor $3$ out of $3 c^{2} d (m^{4})$ .

$\frac{3 (2 k^{2} (2 c^{2} d^{2}))}{3 (c^{2} d (m^{4}))}$

Cancel the common factor.

$\frac{3 (2 k^{2} (2 c^{2} d^{2}))}{3 (c^{2} d (m^{4}))}$

Rewrite the expression.

$\frac{2 k^{2} (2 c^{2} d^{2})}{c^{2} d (m^{4})}$

Step 6

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

Cancel the common factor.

$\frac{2 k^{2} (2 c^{2} d^{2})}{c^{2} d m^{4}}$

Rewrite the expression.

$\frac{2 k^{2} (2 d^{2})}{d (m^{4})}$

Step 7

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

Factor $d$ out of $2 k^{2} (2 d^{2})$ .

$\frac{d (2 k^{2} (2 d))}{d (m^{4})}$

Cancel the common factors.

Cancel the common factor.

$\frac{d (2 k^{2} (2 d))}{d m^{4}}$

Rewrite the expression.

$\frac{2 k^{2} (2 d)}{m^{4}}$

Step 8

Multiply $2$ by $2$ .

$\frac{4 k^{2} d}{m^{4}}$

Simplify ((10mk^2)/(3c^2d))÷((5m^5)/(6c^2d^2))

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