Basic Math Examples

$\frac{{(6 c d^{2})}^{2}}{24 c^{5} d^{4}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $6 c d^{2}$ .

$\frac{{(6 c)}^{2} {(d^{2})}^{2}}{24 c^{5} d^{4}}$

Step 1.2

Apply the product rule to $6 c$ .

$\frac{6^{2} c^{2} {(d^{2})}^{2}}{24 c^{5} d^{4}}$

Step 1.3

Raise $6$ to the power of $2$ .

$\frac{36 c^{2} {(d^{2})}^{2}}{24 c^{5} d^{4}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{36 c^{2} d^{2 \cdot 2}}{24 c^{5} d^{4}}$

Step 1.4.2

Multiply $2$ by $2$ .

$\frac{36 c^{2} d^{4}}{24 c^{5} d^{4}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $36$ and $24$ .

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Step 2.1.1

Factor $12$ out of $36 c^{2} d^{4}$ .

$\frac{12 (3 c^{2} d^{4})}{24 c^{5} d^{4}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $12$ out of $24 c^{5} d^{4}$ .

$\frac{12 (3 c^{2} d^{4})}{12 (2 c^{5} d^{4})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{12 (3 c^{2} d^{4})}{12 (2 c^{5} d^{4})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{3 c^{2} d^{4}}{2 c^{5} d^{4}}$

Step 2.2

Cancel the common factor of $c^{2}$ and $c^{5}$ .

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Step 2.2.1

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

$\frac{c^{2} (3 d^{4})}{2 c^{5} d^{4}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $c^{2}$ out of $2 c^{5} d^{4}$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

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

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{3}{2 c^{3}}$