Algebra Examples

$\frac{4 a^{5}}{7 b^{4}} \cdot \frac{2 b^{2}}{2 a^{4}}$

Step 1

Combine.

$\frac{4 a^{5} (2 b^{2})}{7 b^{4} (2 a^{4})}$

Step 2

Cancel the common factor of $4$ and $2$ .

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Step 2.1

Factor $2$ out of $4 a^{5} (2 b^{2})$ .

$\frac{2 (2 a^{5} (2 b^{2}))}{7 b^{4} (2 a^{4})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $7 b^{4} (2 a^{4})$ .

$\frac{2 (2 a^{5} (2 b^{2}))}{2 (7 b^{4} (a^{4}))}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (2 a^{5} (2 b^{2}))}{2 (7 b^{4} (a^{4}))}$

Step 2.2.3

Rewrite the expression.

$\frac{2 a^{5} (2 b^{2})}{7 b^{4} (a^{4})}$

Step 3

Cancel the common factor of $a^{5}$ and $a^{4}$ .

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Step 3.1

Factor $a^{4}$ out of $2 a^{5} (2 b^{2})$ .

$\frac{a^{4} (2 a (2 b^{2}))}{7 b^{4} (a^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{4}$ out of $7 b^{4} (a^{4})$ .

$\frac{a^{4} (2 a (2 b^{2}))}{a^{4} (7 b^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{a^{4} (2 a (2 b^{2}))}{a^{4} (7 b^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 a (2 b^{2})}{7 b^{4}}$

Step 4

Cancel the common factor of $b^{2}$ and $b^{4}$ .

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Step 4.1

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

$\frac{b^{2} (2 a \cdot (2))}{7 b^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b^{2}$ out of $7 b^{4}$ .

$\frac{b^{2} (2 a \cdot (2))}{b^{2} (7 b^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{b^{2} (2 a \cdot (2))}{b^{2} (7 b^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{2 a \cdot (2)}{7 b^{2}}$

Step 5

Multiply $2$ by $2$ .

$\frac{4 a}{7 b^{2}}$