Basic Math Examples

$a^{2} b^{3} \cdot (2 {(a b)}^{3}) \div a^{3} b^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{a^{2} b^{3} \cdot (2 {(a b)}^{3})}{a^{3} b^{4}}$

Step 2

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

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Step 2.1

Factor $a^{2}$ out of $a^{2} b^{3} \cdot (2 {(a b)}^{3})$ .

$\frac{a^{2} (b^{3} \cdot (2 {(a b)}^{3}))}{a^{3} b^{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a^{2}$ out of $a^{3} b^{4}$ .

$\frac{a^{2} (b^{3} \cdot (2 {(a b)}^{3}))}{a^{2} (a b^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{a^{2} (b^{3} \cdot (2 {(a b)}^{3}))}{a^{2} (a b^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{b^{3} \cdot (2 {(a b)}^{3})}{a b^{4}}$

Step 3

Cancel the common factor of $b^{3}$ and $b^{4}$ .

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Step 3.1

Factor $b^{3}$ out of $b^{3} \cdot (2 {(a b)}^{3})$ .

$\frac{b^{3} (2 {(a b)}^{3})}{a b^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $b^{3}$ out of $a b^{4}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Apply the product rule to $a b$ .

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

Step 5

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

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Step 5.1

Factor $a$ out of $2 a^{3} b^{3}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $a$ out of $a b$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

Factor $b$ out of $2 a^{2} b^{3}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{b (2 a^{2} b^{2})}{b^{1}}$

Step 6.2.2

Factor $b$ out of $b^{1}$ .

$\frac{b (2 a^{2} b^{2})}{b \cdot 1}$

Step 6.2.3

Cancel the common factor.

$\frac{b (2 a^{2} b^{2})}{b \cdot 1}$

Step 6.2.4

Rewrite the expression.

$\frac{2 a^{2} b^{2}}{1}$

Step 6.2.5

Divide $2 a^{2} b^{2}$ by $1$ .

$2 a^{2} b^{2}$