Basic Math Examples

$\frac{4 a^{2}}{9 b^{2} c^{4}} \cdot \frac{8 c}{3 b \cdot (3 a)} \cdot \frac{3 c}{a^{2} b}$

Step 1

Combine.

$\frac{4 a^{2} (8 c)}{9 b^{2} c^{4} (3 b \cdot (3 a))} \cdot \frac{3 c}{a^{2} b}$

Step 2

Combine.

$\frac{4 a^{2} (8 c) (3 c)}{9 b^{2} c^{4} (3 b \cdot (3 a)) (a^{2} b)}$

Step 3

Multiply $c$ by $c$ by adding the exponents.

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Step 3.1

Move $c$ .

$\frac{4 a^{2} (8 (c \cdot c)) \cdot 3}{9 b^{2} c^{4} (3 b \cdot (3 a)) (a^{2} b)}$

Step 3.2

Multiply $c$ by $c$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{2} c^{4} (3 b \cdot (3 a)) (a^{2} b)}$

Step 4

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

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Step 4.1

Move $b$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 (b \cdot b^{2}) c^{4} (3 \cdot (3 a)) (a^{2} b)}$

Step 4.2

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

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Step 4.2.1

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 (b^{1} b^{2}) c^{4} (3 \cdot (3 a)) (a^{2} b)}$

Step 4.2.2

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{1 + 2} c^{4} (3 \cdot (3 a)) (a^{2} b)}$

Step 4.3

Add $1$ and $2$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{3} c^{4} (3 \cdot (3 a)) (a^{2} b)}$

Step 5

Multiply $b^{3}$ by $b$ by adding the exponents.

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Step 5.1

Move $b$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 (b \cdot b^{3}) c^{4} (3 \cdot (3 a)) a^{2}}$

Step 5.2

Multiply $b$ by $b^{3}$ .

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Step 5.2.1

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 (b^{1} b^{3}) c^{4} (3 \cdot (3 a)) a^{2}}$

Step 5.2.2

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{1 + 3} c^{4} (3 \cdot (3 a)) a^{2}}$

Step 5.3

Add $1$ and $3$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 a)) a^{2}}$

Step 6

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

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Step 6.1

Move $a^{2}$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 (a^{2} a)))}$

Step 6.2

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

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Step 6.2.1

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 (a^{2} a^{1})))}$

Step 6.2.2

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

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 a^{2 + 1}))}$

Step 6.3

Add $2$ and $1$ .

$\frac{4 a^{2} (8 c^{2}) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 a^{3}))}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

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

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Step 7.1.1

Factor $a^{2}$ out of $4 a^{2} (8 c^{2}) \cdot 3$ .

$\frac{a^{2} ((4 (8 c^{2})) \cdot 3)}{9 b^{4} c^{4} (3 \cdot (3 a^{3}))}$

Step 7.1.2

Cancel the common factors.

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Step 7.1.2.1

Factor $a^{2}$ out of $9 b^{4} c^{4} (3 \cdot (3 a^{3}))$ .

$\frac{a^{2} ((4 (8 c^{2})) \cdot 3)}{a^{2} (9 b^{4} c^{4} (3 \cdot (3 a)))}$

Step 7.1.2.2

Cancel the common factor.

$\frac{a^{2} ((4 (8 c^{2})) \cdot 3)}{a^{2} (9 b^{4} c^{4} (3 \cdot (3 a)))}$

Step 7.1.2.3

Rewrite the expression.

$\frac{(4 (8 c^{2})) \cdot 3}{9 b^{4} c^{4} (3 \cdot (3 a))}$

Step 7.2

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

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Step 7.2.1

Factor $c^{2}$ out of $(4 (8 c^{2})) \cdot 3$ .

$\frac{c^{2} ((4 \cdot (8)) \cdot 3)}{9 b^{4} c^{4} (3 \cdot (3 a))}$

Step 7.2.2

Cancel the common factors.

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Step 7.2.2.1

Factor $c^{2}$ out of $9 b^{4} c^{4} (3 \cdot (3 a))$ .

$\frac{c^{2} ((4 \cdot (8)) \cdot 3)}{c^{2} (9 b^{4} c^{2} (3 \cdot (3 a)))}$

Step 7.2.2.2

Cancel the common factor.

$\frac{c^{2} ((4 \cdot (8)) \cdot 3)}{c^{2} (9 b^{4} c^{2} (3 \cdot (3 a)))}$

Step 7.2.2.3

Rewrite the expression.

$\frac{(4 \cdot (8)) \cdot 3}{9 b^{4} c^{2} (3 \cdot (3 a))}$

Step 7.3

Cancel the common factor of $3$ and $9$ .

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Step 7.3.1

Factor $3$ out of $(4 \cdot (8)) \cdot 3$ .

$\frac{3 \cdot (4 \cdot (8))}{9 b^{4} c^{2} (3 \cdot (3 a))}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $9 b^{4} c^{2} (3 \cdot (3 a))$ .

$\frac{3 \cdot (4 \cdot (8))}{3 (3 b^{4} c^{2} (3 \cdot (3 a)))}$

Step 7.3.2.2

Cancel the common factor.

$\frac{3 \cdot (4 \cdot (8))}{3 (3 b^{4} c^{2} (3 \cdot (3 a)))}$

Step 7.3.2.3

Rewrite the expression.

$\frac{4 \cdot (8)}{3 b^{4} c^{2} (3 \cdot (3 a))}$

Step 8

Multiply $4$ by $8$ .

$\frac{32}{3 b^{4} c^{2} \cdot 3 \cdot 3 a}$

Step 9

Simplify the denominator.

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Step 9.1

Multiply $3$ by $3$ .

$\frac{32}{9 b^{4} c^{2} \cdot 3 a}$

Step 9.2

Multiply $3$ by $9$ .

$\frac{32}{27 b^{4} c^{2} a}$