Precalculus Examples

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

Step 1

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

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Step 1.1

Factor $c$ out of $c^{4} d^{3}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $c$ out of $c d^{2}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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Step 2.1

Factor $d^{2}$ out of $c^{3} d^{3}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{d^{2} (c^{3} d)}{d^{2} \cdot 1} {(\frac{d^{2}}{c^{3}})}^{3}$

Step 2.2.2

Cancel the common factor.

$\frac{d^{2} (c^{3} d)}{d^{2} \cdot 1} {(\frac{d^{2}}{c^{3}})}^{3}$

Step 2.2.3

Rewrite the expression.

$\frac{c^{3} d}{1} {(\frac{d^{2}}{c^{3}})}^{3}$

Step 2.2.4

Divide $c^{3} d$ by $1$ .

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

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{d^{2}}{c^{3}}$ .

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

Step 3.2

Multiply the exponents in ${(d^{2})}^{3}$ .

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Step 3.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$c^{3} d \frac{d^{2 \cdot 3}}{{(c^{3})}^{3}}$

Step 3.2.2

Multiply $2$ by $3$ .

$c^{3} d \frac{d^{6}}{{(c^{3})}^{3}}$

Step 3.3

Multiply the exponents in ${(c^{3})}^{3}$ .

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Step 3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$c^{3} d \frac{d^{6}}{c^{3 \cdot 3}}$

Step 3.3.2

Multiply $3$ by $3$ .

$c^{3} d \frac{d^{6}}{c^{9}}$

Step 4

Cancel the common factor of $c^{3}$ .

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Step 4.1

Factor $c^{3}$ out of $c^{3} d$ .

$c^{3} (d) \frac{d^{6}}{c^{9}}$

Step 4.2

Factor $c^{3}$ out of $c^{9}$ .

$c^{3} (d) \frac{d^{6}}{c^{3} c^{6}}$

Step 4.3

Cancel the common factor.

$c^{3} d \frac{d^{6}}{c^{3} c^{6}}$

Step 4.4

Rewrite the expression.

$d \frac{d^{6}}{c^{6}}$

Step 5

Combine $d$ and $\frac{d^{6}}{c^{6}}$ .

$\frac{d \cdot d^{6}}{c^{6}}$

Step 6

Multiply $d$ by $d^{6}$ by adding the exponents.

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Step 6.1

Multiply $d$ by $d^{6}$ .

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Step 6.1.1

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

$\frac{d^{1} d^{6}}{c^{6}}$

Step 6.1.2

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

$\frac{d^{1 + 6}}{c^{6}}$

Step 6.2

Add $1$ and $6$ .

$\frac{d^{7}}{c^{6}}$