Basic Math Examples

${(4 c^{5} d \div 16 c d^{4})}^{3}$

Step 1

Rewrite the division as a fraction.

${(\frac{4 c^{5} d}{16 c d^{4}})}^{3}$

Step 2

Cancel the common factor of $4$ and $16$ .

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Step 2.1

Factor $4$ out of $4 c^{5} d$ .

${(\frac{4 (c^{5} d)}{16 c d^{4}})}^{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $16 c d^{4}$ .

${(\frac{4 (c^{5} d)}{4 (4 c d^{4})})}^{3}$

Step 2.2.2

Cancel the common factor.

${(\frac{4 (c^{5} d)}{4 (4 c d^{4})})}^{3}$

Step 2.2.3

Rewrite the expression.

${(\frac{c^{5} d}{4 c d^{4}})}^{3}$

Step 3

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

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Step 3.1

Factor $c$ out of $c^{5} d$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $\frac{c^{4}}{4 d^{3}}$ .

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

Step 5.2

Apply the product rule to $4 d^{3}$ .

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

Step 6

Multiply the exponents in ${(c^{4})}^{3}$ .

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Step 6.1

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

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

Step 6.2

Multiply $4$ by $3$ .

$\frac{c^{12}}{4^{3} {(d^{3})}^{3}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $4$ to the power of $3$ .

$\frac{c^{12}}{64 {(d^{3})}^{3}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{c^{12}}{64 d^{3 \cdot 3}}$

Step 7.2.2

Multiply $3$ by $3$ .

$\frac{c^{12}}{64 d^{9}}$