Simplify (cy^3)/(12d^3k^3)-(4w)/(9cd^2)

$\frac{c y^{3}}{12 d^{3} k^{3}} - \frac{4 w}{9 c d^{2}}$

To write $\frac{c y^{3}}{12 d^{3} k^{3}}$ as a fraction with a common denominator, multiply by $\frac{3 c}{3 c}$ .

$\frac{c y^{3}}{12 d^{3} k^{3}} \cdot \frac{3 c}{3 c} - \frac{4 w}{9 c d^{2}}$

To write $- \frac{4 w}{9 c d^{2}}$ as a fraction with a common denominator, multiply by $\frac{4 d k^{3}}{4 d k^{3}}$ .

$\frac{c y^{3}}{12 d^{3} k^{3}} \cdot \frac{3 c}{3 c} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Write each expression with a common denominator of $36 c d^{3} k^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{c y^{3}}{12 d^{3} k^{3}}$ and $\frac{3 c}{3 c}$ .

$\frac{c y^{3} (3 c)}{12 d^{3} k^{3} (3 c)} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Multiply $3$ by $12$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Multiply $\frac{4 w}{9 c d^{2}}$ and $\frac{4 d k^{3}}{4 d k^{3}}$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{9 c d^{2} (4 d k^{3})}$

Multiply $4$ by $9$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{2} (d k^{3})}$

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

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c (d^{1} d^{2}) k^{3}}$

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

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{1 + 2} k^{3}}$

Add $1$ and $2$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{3} k^{3}}$

Reorder the factors of $36 c d^{3} k^{3}$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Combine the numerators over the common denominator.

$\frac{c y^{3} (3 c) - 4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Simplify the numerator.

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Rewrite using the commutative property of multiplication.

$\frac{3 (c y^{3}) c - 4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Multiply $c$ by $c$ by adding the exponents.

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Move $c$ .

$\frac{3 (c \cdot c y^{3}) - 4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Multiply $c$ by $c$ .

$\frac{3 (c^{2} y^{3}) - 4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Multiply $4$ by $- 4$ .

$\frac{3 c^{2} y^{3} - 16 w d k^{3}}{36 d^{3} k^{3} c}$

Simplify (cy^3)/(12d^3k^3)-(4w)/(9cd^2)

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