Pre-Algebra Examples

$\frac{6 a^{2} b}{15 c^{2} d^{2}} \cdot \frac{5 c d a^{3}}{a^{2} b^{2}}$

Step 1

Combine.

$\frac{6 a^{2} b (5 c d a^{3})}{15 c^{2} d^{2} (a^{2} b^{2})}$

Step 2

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

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Step 2.1

Move $a^{3}$ .

$\frac{6 (a^{3} a^{2}) b (5 c d)}{15 c^{2} d^{2} (a^{2} b^{2})}$

Step 2.2

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

$\frac{6 a^{3 + 2} b (5 c d)}{15 c^{2} d^{2} (a^{2} b^{2})}$

Step 2.3

Add $3$ and $2$ .

$\frac{6 a^{5} b (5 c d)}{15 c^{2} d^{2} (a^{2} b^{2})}$

Step 3

Cancel the common factor of $6$ and $15$ .

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Step 3.1

Factor $3$ out of $6 a^{5} b (5 c d)$ .

$\frac{3 (2 a^{5} b (5 c d))}{15 c^{2} d^{2} (a^{2} b^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $15 c^{2} d^{2} (a^{2} b^{2})$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{2 a^{5} b (5 c d)}{5 c^{2} d^{2} (a^{2} b^{2})}$

Step 4

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

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Step 4.1

Factor $a^{2}$ out of $2 a^{5} b (5 c d)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $5 c^{2} d^{2} (a^{2} b^{2})$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

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Step 8.1

Factor $d$ out of $2 a^{3} (d)$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{2 a^{3}}{c d b}$