Basic Math Examples

$(\frac{2 a^{3}}{3 b^{2}}) (\frac{6 b}{a}) \div \frac{4 a^{2}}{b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{2 a^{3}}{3 b^{2}}) (\frac{6 b}{a}) \frac{b}{4 a^{2}}$

Step 2

Combine.

$\frac{2 a^{3} (6 b)}{3 b^{2} a} \cdot \frac{b}{4 a^{2}}$

Step 3

Combine.

$\frac{2 a^{3} (6 b) b}{3 b^{2} a (4 a^{2})}$

Step 4

Multiply $b$ by $b$ by adding the exponents.

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Step 4.1

Move $b$ .

$\frac{2 a^{3} (6 (b \cdot b))}{3 b^{2} a (4 a^{2})}$

Step 4.2

Multiply $b$ by $b$ .

$\frac{2 a^{3} (6 b^{2})}{3 b^{2} a (4 a^{2})}$

Step 5

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

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Step 5.1

Move $a^{2}$ .

$\frac{2 a^{3} (6 b^{2})}{3 b^{2} (a^{2} a) \cdot 4}$

Step 5.2

Multiply $a^{2}$ by $a$ .

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Step 5.2.1

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

$\frac{2 a^{3} (6 b^{2})}{3 b^{2} (a^{2} a^{1}) \cdot 4}$

Step 5.2.2

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

$\frac{2 a^{3} (6 b^{2})}{3 b^{2} a^{2 + 1} \cdot 4}$

Step 5.3

Add $2$ and $1$ .

$\frac{2 a^{3} (6 b^{2})}{3 b^{2} a^{3} \cdot 4}$

Step 6

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

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Step 6.1

Factor $2$ out of $2 a^{3} (6 b^{2})$ .

$\frac{2 (a^{3} (6 b^{2}))}{3 b^{2} a^{3} \cdot 4}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{2 (a^{3} (6 b^{2}))}{2 (3 b^{2} a^{3} \cdot 2)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (a^{3} (6 b^{2}))}{2 (3 b^{2} a^{3} \cdot 2)}$

Step 6.2.3

Rewrite the expression.

$\frac{a^{3} (6 b^{2})}{3 b^{2} a^{3} \cdot 2}$

Step 7

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

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Step 7.1

Cancel the common factor.

$\frac{a^{3} (6 b^{2})}{3 b^{2} a^{3} \cdot 2}$

Step 7.2

Rewrite the expression.

$\frac{6 b^{2}}{3 b^{2} \cdot 2}$

Step 8

Cancel the common factor of $6$ and $3$ .

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Step 8.1

Factor $3$ out of $6 b^{2}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{2 b^{2}}{b^{2} \cdot 2}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Cancel the common factor.

$\frac{2 b^{2}}{b^{2} \cdot 2}$

Step 9.2

Rewrite the expression.

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

Step 10

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

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Step 10.1

Cancel the common factor.

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

Step 10.2

Rewrite the expression.

$1$